MAT 300 Unit 4 Challenges Sophia MAT300 Unit 4 Challenges Sophia

MAT 300 Unit 4 Challenges Sophia Click below link for Answers https://www.sobtell.com/q/tutorial/default/206486-mat-300-unit-4-challenges-sophia https://www.sobtell.com/q/tutorial/default/206486-mat-300-unit-4-challenges-sophia

CHALLENEG 1 Mr. Carl Burl, an artist, has recorded the number of visitors who visited his exhibit in the first 8 hours of opening day. He has made a scatter plot to depict the relationship between the number of hours and the number of visitors.

How many visitors came to his exhibition in the first 3 hours? a.)

16 visitors b.)

6 visitors c.)

7 visitors d.)

22 visitors  In order to get the total number of visitors in the first 3 hours, we need to sum up the visitors at 1, 2, and 3 hours.

In the first hour, there were four visitors.

In the second hour, there were five visitors.

In the third hour, there were seven visitors.

Add the visitors together to get 4+5+7 = 16 total visitors in the first 3 hours.

Robert is wondering if there is an association between the number of hours he studies and the number of semester credits he is enrolled in. The information is shown in the scatterplot below.

If Robert is enrolled in five-semester credits, how many hours did he study? a.)

4 hours b.)

3 hours c.)

6 hours

d.)

9 hours  In order to assess how many hours he studied, we go to the semester credit axis and go between 4 and 6, as this is where the value of 5 would be. At this point we see that the corresponding value, when the semester credit is 5, would be on the vertical line for 6 hours of study.

Glen Sarin is a photographer who is wondering if there is an association between the number of photographs she takes and percent cloud coverage. Her record is shown in the scatterplot.

How many photographs did she take when the cloud coverage was 4 percent or less? a.)

900 photographs b.)

1050 photographs c.)

750 photographs d.)

150 photographs  In order to get the total photographs when cloud coverage was 4 percent or less, we add up all the values from 0 to 4.

At 4%, there were 150 photographs.

At 3%, there were 200 photographs.

At 2%, there were 250 photographs.

At 1%, there were 150 photographs.

The total number of photographs should be 150 + 200 + 250 + 150 = 750 photographs.

The following scatterplot shows the 20 top-selling cars with their weight on the horizontal axis and their miles per gallon (mpg) on the vertical axis.

The overall direction of this data is __________. The strength of the association is __________. a.) positive; weak b.) negative; weak c.) positive; strong d.) negative; strong  Since the relationship of a potential trend line is downward sloping, it is a negative relationship. Most of the points would lie relatively close to the line, so it would be strong.

The following scatterplot relates the life expectancy of animals to their heart rate.

Ignoring humans (which are labeled "Man" in the scatterplot), which two conclusions can be made from the scatterplot? a.)

The strength of the association is moderate. b.)

The overall direction of data is negative. c.)

The strength of the association is strong. d.)

The overall direction of the data is positive. e.)

The strength of the association is weak. f.)

The overall direction of the data is non-linear. Answer Rationale The direction of the trend line is downward, so there is a negative trend. Since most of the points lie around the trend line, we can say there is a strong relationship.

The following scatterplot shows the 20 top-selling cars with their weight on the horizontal axis and their miles per gallon (mpg) on the vertical axis.

The overall direction of this data is __________. The strength of the association is __________. a.) negative; weak b.) negative; strong c.) positive; strong d.) positive; weak  Since the relationship of a potential trend line is downward sloping, it is a negative relationship. Most of the points would lie relatively close to the line, so it would be strong.

Tasha found the following scatterplot that shows four different compact cars at different speeds, from 20 to 70 mph.

Which answer choice correctly indicates the explanatory variable and the response variable? a.)

Explanatory variable: MPG Response variable: MPH b.)

Explanatory variable: Cars Response variable: MPG c.)

Explanatory variable: MPH Response variable: Cars d.)

Explanatory variable: MPH Response variable: MPG  The explanatory variable is the variable along the horizontal axis, which is MPH. The outcome or response variable is the variable along the vertical axis, which is MPG. Simone, a veterinary student, recently discovered the following scatterplot produced by the Department of Agriculture.

Which answer choice correctly indicates the explanatory variable and the response variable? a.)

Explanatory variable: Weight Response variable: Weekly feed cost b.)

Explanatory variable: Animals Response variable: Weekly feed cost c.)

Explanatory variable: Weekly feed cost Response variable: Weight d.)

Explanatory variable: Weekly feed cost Response variable: Animals  The explanatory variable is the variable along the horizontal axis, which is weekly feed cost.

The outcome or response variable is the variable along the vertical axis, which is weight. hawna reads a study about exercise that includes the following scatterplot.

Which answer choice correctly indicates the explanatory variable and the response variable? a.)

Explanatory variable: Exercise Response variable: Calories burned per minute b.)

Explanatory variable: Weight Response variable: Exercise c.)

Explanatory variable: Weight Response variable: Calories burned per minute d.)

Explanatory variable: Calories burned per minute Response variable: Weight  The explanatory variable is the variable along the horizontal axis, which is weight. The outcome or response variable is the variable along the vertical axis, which is calories burned per minute.

Select the statement about the correlation coefficient (r) that is TRUE. a.)

The correlation coefficient cannot be calculated by hand. A statistical software must be used. b.)

The stronger the strength of association, the lower the value of the correlation coefficient. c.)

The correlation coefficient is always between -1 and +1. d.)

The correlation coefficient r = 0.75 shows a strong positive relationship between two variables.  Recall that correlation is bound between -1 and 1. Values that get closer to 1 or -1 mean strong relationships in the negative or positive direction. Values close to 0 mean variables have no linear association.

Select the FALSE statement about the correlation coefficient (r). a.)

The sign of the correlation coefficient tells us if the pair of variables is positively or negatively associated. b.)

The value of the correlation coefficient lies between -1 and 1. c.)

The correlation coefficient r = 0 shows that two variables are strongly correlated. d.)

The correlation coefficient quantifies the strength of the linear relationship between two variables.  Recall that correlation is bound between -1 and 1. Values that get closer to 1 or -1 would indicate strong relationships in the negative or positive direction. Values close to 0 would indicate that the variables have no linear association.

Select the statement regarding the correlation coefficient (r) that is TRUE. a.)

The sign of the correlation coefficient might change when we combine two subgroups of data. b.)

A correlation coefficient of 1 implies a weak correlation between two variables. c.)

Correlation coefficient cannot be calculated for all scatterplots. d.)

The correlation coefficient describes the direction of the association between two variables.  When combining data, it may be the case that when combining the data, the direction of the relationship might change. A good example of this is Simpson's paradox, which illustrates that subgroup analysis yields different relationships than the overall group.

The test scores of five students in both Math and Geography are presented in the table.

The calculation for the correlation, r, for this set of five students is __________. Answer choices are rounded to the hundredths place a.)

0.45 b.)

0.32

c.)

0.57 d.)

0.10  To find the correlation, it is recommended to use a spreadsheet like Excel. First, enter the values into separate columns, one for Math and one for Geography. Then type the function =CORREL, highlight each column, and hit enter. This will give a correlation of 0.32.

A local shop's sales of ice cream and sales of sunglasses are presented in the table.

The calculation for the correlation, r, for this set of five data points is __________. Answer choices are rounded to the hundredths place. a.)

0.98 b.)

0.94 c.)

0.77 d.)

0.88  To find the correlation, it is recommended to use a spreadsheet like Excel. First, enter the values into separate columns, one for Ice Cream and one for Sunglasses. Then type the function =CORREL, highlight each column, and hit enter. This will give a correlation of 0.94.

ASDF Correct Average height and average weight of five students are presented in the table.

The calculation for the correlation, r, for this set of five students is __________. Answer choices are rounded to the hundredths place. a.)

0.70 b.)

0.84 c.)

0.91 d.)

0.49 

To find the correlation, it is recommended to use a spreadsheet like Excel. First, enter the values into separate columns, one for Height and one for Weight. Then type the function =CORREL, highlight each column, and hit enter. This will give a correlation of 0.70.

CHALLENEG 2 Which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.)

Number of miles driven; Number of radio stations listened to b.)

Average annual temperature in the United States; Annual sweater sales by an American retailer c.)

Age of baby; Weight of baby d.)

Number of minutes spent exercising; Number of calories burned  For a negative correlation, we would expect as the value of one variable goes up, the other goes down. As the annual temperature goes up, people would need less thick clothes, so sales of sweaters should go down.

Correct Which of the following data sets would most likely have a positive association and a correlation coefficient between 0 and 1? a.)

Number of months Lela owns a car; Number of scratches on Lela's car b.)

Speed of Frank's vehicle; Time it takes Frank to arrive at destination c.)

Number of school absences; Test scores in school d.)

Level of education; Head circumference  For a positive correlation, we would expect as the value of one variable goes up, the other also goes up. As number of months Lela owns a car increases, the chances of wear and tear increases, so the number of scratches also goes up.

Which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.)

Swimsuit Sales throughout the year; Sunscreen Sales throughout the year b.)

Number of miles driven by Paul; Number of gallons of gas used by Paul's car c.)

Steepness of the Appalachian Trail; John's speed while hiking the Appalachian trail d.)

Average seasonal temperature in the United States; Air-conditioning costs for homes in the United States  For a negative correlation, we would expect as the value of one variable goes up, the other goes down. As steepness of a trail increases, the trail is harder to climb, so the speed going up it should go down.

A researcher found a study relating the mortality rates for women aged 65 to 74, y, to the proportion of calories from sweeteners in their diets, x. When researchers looked at the association of x and y, they found that the coefficient of determination was .

Select two conclusions that the researcher can make from this data. a.)

About 51% of the variation in mortality rates is explained by a linear relationship with proportion of calories in sweeteners. b.)

About 70% of the variation in proportion of calories in sweeteners is explained by a linear relationship with mortality rates. c.)

The correlation coefficient, r, is 0.236. d.)

The correlation coefficient, r, is 0.514. e.)

About 49% of the variation in mortality rates is explained by a linear relationship with the proportion of calories in sweeteners. f.)

The correlation coefficient, r, is 0.697. Answer Rationale Recall the coefficient of determination is a measure of the percent of variation in the outcome, y, explained by a regression. So this means that 48.6%, or about 49%, of the variation in the mortality rates for women aged 65 to 74, y, can be accounted for by the proportion of calories they get from sweeteners, x.

Also, in order to get the correlation, we simply take the square root of r-squared: A researcher found a study relating the distance a driver can see, y, to the age of the driver, x.

When researchers looked at the association of x and y, they found that the coefficient of determination was .

Select two conclusions that the researcher can make from this data. a.)

The correlation coefficient, r, is -0.271. b.)

The correlation coefficient, r, is -0.458. c.)

About 74% of the variation in the driver's age is explained by a linear relationship with the distance that the driver can see. d.)

About 46% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. e.)

The correlation coefficient, r, is -0.736. f.)

About 54% of the variation in distance that the driver can see is explained by a linear relationship with the driver's age. Answer Rationale Recall the coefficient of determination is a measure of the percent of variation in the outcome, y, explained by a regression. So this means that 54.2%, or about 54%, of the variation in the value of how far a driver can see, y, can be accounted for by the age of the driver, x.

Also, in order to get the correlation, we simply take the square root of r-squared: We can also note that the correlation should be negative since age and how far a driver can see should be negatively related, so it should be: A researcher found a study relating the value of a car, y, to the age of the car, x. When researchers looked at the association of x and y, they found that the coefficient of determination was .

Select two conclusions that the researcher can make from this data. a.)

About 16% of the variation in value of the car is explained by a linear relationship with the age of the car. b.)

The correlation coefficient, r, is 0.397. c.)

About 40% of the variation in the age of the car is explained by a linear relationship with the value of the car. d.)

The correlation coefficient, r, is 0.842. e.)

About 84% of the variation in the value of the car is explained by a linear relationship with the age of the car. f.)

The correlation coefficient, r, is 0.025. Answer Rationale Recall the coefficient of determination is a measure of the percent of variation in the outcome, y, explained by a regression. So this means that 15.8%, or about 16%, of the variation in the value of a car (y) can be accounted for by the age of the car (x).

Also, in order to get the correlation coefficient, we simply take the square root of r-squared:

A scatterplot was created using the miles-per-gallon and weight of 20 cars. Another car is added to the scatterplot (shown in red in the lower part of the graph).

Which statement is TRUE regarding the added point? a.)

It is an outlier in the y-direction. b.)

It is not an outlier. c.)

It is an outlier in the x-direction. d.)

It is an outlier in both the x- and y-direction.  The data is well within the data in the x-direction along the horizontal axis, but it is below the range of data in the vertical axis, lying below the other data points. So it is an outlier in the ydirection.

A scatterplot was created using the miles-per-gallon and weight of 8 cars. Another car is added to the scatterplot (shown in red in the left side of the graph).

Select the TRUE statement about this added point. a.)

It is not an outlier. b.)

It is an outlier in both the x- and y-direction. c.)

It is an outlier in the y-direction. d.)

It is an outlier in the x-direction.  Since the data is within the range of the y-values (along the vertical axis), it is not an outlier in the y-direction. The data is however, far away along the horizontal axis or x-direction.

A scatterplot was created using the weight and weekly feed cost for eight pets. Two more pets are added to the scatterplot (shown in red in the upper left side of the graph).

Select the TRUE statement about the two added points. a.)

They are outliers in both the x- and y-direction. b.)

They are not outliers. c.)

They are outliers in the x-direction. d.)

They are outliers in the y-direction.  Since these values are outside of the other data in the x and y direction, these are outliers in both the x and y direction.

A data set was graphed using a scatterplot.

The correlation coefficient, r, is 0.845.

Which of the following statements explains how the correlation is affected? a.)

It is affected by inappropriate grouping. b.)

It is not affected. c.)

It is affected by non-linearity. d.)

It is affected by an influential point.  Recall that correlation is a measure of linear association. It is not a good measure of how data is related if the relationship is non-linear. The graph shown is clearly non-linear and correlation would not be a good measure of association.

A data set was graphed using a scatterplot.

The correlation coefficient, r, is 0.192.

Which of the following statements explains how the correlation is affected? a.)

It is not affected. b.)

It is affected by non-linearity. c.)

It is affected by an influential point. d.)

It is affected by inappropriate grouping.  Since there are gaps in the data, really illustrating 3 separate groups rather than 1 overall group would be an inappropriate grouping. By exploring correlation overall it will underestimate how closely related the data is within each group.

Correct Go to the Next Concept A data set was graphed using a scatterplot.

The correlation coefficient, r, is 0.813.

Which of the following statements explains how the correlation is affected? a.)

It is not affected. b.)

It is affected by inappropriate grouping. c.)

It is affected by an influential point. d.)

It is affected by non-linearity. 

Since correlation is affected by all of the points, an outlier that lies away from data that is otherwise closely related, will underestimate how close the relationship is. So this illustrates how correlation is affected by an influential outlier.

Which of the following statements is FALSE? a.)

A correlation coefficient of 1 could mean that the relationship is just a coincidence. b.)

A controlled experiment can give the best evidence for causation. c.)

A correlation between -1 and 1 establishes a relationship, but not necessarily a causation. d.)

A high correlation between the explanatory and response variables is sufficient to prove causation.  Recall for causation, correlation is a necessary, but not a sufficient condition, meaning for something to be causal there must be a high correlation. However, if there is a high correlation that doesn't mean it is causal. In some cases, simple coincidences can create a high correlation where a causation does not exist. For example, people who live in large metro areas might get into less accidents per capita, however that might simply be because those who live in large metro areas drive less.

Which of the following statements is TRUE? a.)

High correlation does not always establish causation. b.)

A high correlation means that the response variable is caused by the explanatory variable. c.)

Low correlation implies causation. d.)

To imply causation, the correlation must be 1.  Correlation simply measures association. Causation means one variable directly influences another and is a much more strict condition.

Which of the following statements is TRUE? a.)

A high correlation indicates that explanatory variable is a direct cause of the response variable. b.)

Having a low correlation is sufficient enough to imply causation. c.)

To imply causation, the correlation must be -1. d.)

A high correlation can indicate a relationship but cannot prove causation.  Recall correlation doesn't necessarily mean causation. More conditions are required for causation. For causation a direct relationship must be realized, which cannot be proven by correlation alone.

Correct Go to the Next Concept

Stephanie knows that a correlation between the number of bars and the number of churches in her city does not, in itself, mean that more bars will lead to a higher number of churches.

Which of the following would NOT be a lurking variable in the above scenario? a.)

Population density b.)

The time of day that Stephanie attends service c.)

The city's budget d.)

Stephanie's proximity to the center of the city  A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely the time that you attend service is related to the number of bars in a given area.

Correct hawna knows that a correlation between calories of sweeteners consumed and mortality rates among women does not, in itself, mean that drinking more soft drinks will lead to a higher chance of her dying.

Which of the following would NOT be a lurking variable in the above scenario? a.)

The time of day Shawna exercises b.)

Shawna's weight c.)

The amount of caffeine available in soft drinks d.)

The number of soft drink brands available for purchase  A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely the time that your exercise is related to mortality or how much sweetener you consume.

Steve knows that a correlation between diet and exercise compared to his blood pressure does not, in itself, mean that diet and exercise will lead to lower blood pressure.

Which of the following would NOT be a lurking variable in the above scenario? a.)

The time of day that Steve diets b.)

Steve's stress level c.)

The amount of cigarettes that Steve smokes d.)

Steve's occupation 

A variable is a lurking variable if it can influence an explanatory/response relationship. So it must be related to both the explanatory and response variable. It is not likely the time that your diet is related to the overall blood pressure or the amount you diet and exercise.

Correct Go to the Next Concept Smoking causes lung cancer.

Which of the following is necessary to establish causality for the above claim? a.)

Use only an observational study to show that smoking causes lung cancer. b.)

Not considering other possible causes of lung cancer. c.)

Look for cases where correlation between smoking and lung cancer remains while other variables vary. d.)

Keep all variables the same to get duplicate results.  One of the key components of causality is that a correlation remains even when controlling for other factors. So when other factors change, if there is still a correlation between smoking and lung cancer it would support that cause and effect relationship.

Increased sugar intake leads to higher levels of body fat.

Which of the following is NOT necessary to establish causality? a.)

Look for evidence that greater amounts of sugar intake produces higher levels of body fat. b.)

Complete a randomized trial. c.)

Check if higher levels of body fat is present or absent when increased sugar is present or absent. d.)

Determine the physical mechanism for cause-and-effect.  For causality, it is the case that a dose-response effect helps to prove it. However, with something like body fat, which is probably caused by many factors, the absence of this relationship doesn't mean it is not causal.

Thirty minutes of exercise per day can reduce your blood pressure.

Which of the following is a guideline for establishing causality? a.)

Look for evidence that smaller amounts of exercise produces a reduction in blood pressure. b.)

Control the number of minutes of exercise and blood pressure to get the same results. c.)

Check if lower blood pressure is present or absent when exercise is present or absent. d.)

Perform a randomized, controlled experiment. 

A randomized controlled experiment is one of the best ways to establish causality. It allows you to check to see if an effect is present or absent when a treatment is present or absent.

Correct CHLLENAEG A consulting firm records their employees' income against the number of hours worked in the scatterplot shown below.

Using the best-fit line, which of the following predictions is TRUE? a.)

An employee would earn $310 if they work for 7 hours on a project. b.)

An employee would earn $730 if they work for 27 hours on a project. c.)

An employee would earn about $470 if they work for 15 hours on a project. d.)

An employee would earn $370 if they work for 10 hours on a project.  The line of best fit can be used to get predictions. So if we look at particular number of hours of work, we can get a predicted amount earned based on the corresponding value on the bestfit line. If we look at 15 hours of work, then the predicted amount looks to be about $470 The cost of electricity per unit usage can be seen in the scatterplot shown below.

Using the best-fit line, which of the following predictions is TRUE? a.)

An electricity bill for 9 units would cost $11. b.)

An electricity bill for 23 units would cost $38. c.)

An electricity bill for 11 units would cost $19. d.)

An electricity bill for 16 units would cost $24.  The line of best fit can be used to get predictions. So if we look at a particular number of units, we can get a predicted bill charge based on the corresponding value on the best-fit line.

If we look at 16 units, then the predicted bill looks to be about $24.

Jack's father has recorded the amount of time his son has played video games for the last 7 days. The corresponding scatterplot is shown below Using the best-fit line, which of the following predictions is TRUE? a.)

Jack devoted 38 minutes to playing video games after 1 day. b.)

Jack devoted 50 minutes to playing video games after 6 days. c.)

Jack devoted 64 minutes to playing video games after 8 days. d.)

Jack devoted 41 minutes to playing video games after 2 days.

 The line of best fit can be used to get predictions. So if we look at a particular day, we can get a predicted time based on the corresponding value on the best-fit line. If we look at Day 8, then the predicted time looks to be about 64 minutes.

Cynthia has measured the weight and miles per gallon of four different cars. The points fall closely on a line.

Using the data values that Cynthia collected, select the correct slope and y-intercept. a.) b.) c.) d.)  In order to get slope, we can use the formula: We can pick any 2 points, such as (5, 32) and (10, 27). We can note that: The y-intercept is the corresponding y-value when x=0. To find this using the information that we have, we can use the linear equation and plug in one point, such as (5,32), for x and y, and the slope, -1, for m, and solve for the y-intercept, b: The y-intercept would be at 37.

Robert has measured the engine speed and horsepower of four different sports cars. The points fall closely on a line.

Using the data values that Robert collected, select the correct slope and y-intercept. a.) b.)

c.) d.)  In order to get slope, we can use the formula: .

We can pick any 2 points, such as (2, 80) and (4, 160). We can note that: The y-intercept is the corresponding y-value when x=0. To find this using the information that we have, we can use the linear equation and plug in one point, such as (2,80), for x and y, and the slope, 40, for m, and solve for the y-intercept, b: The y-intercept would be at 0.

Pete has measured the diameter and circumference of four different tires. The points fall closely on a line.

Using the data values that Pete collected, select the correct slope and y-intercept. a.) b.) c.) d.)  In order to get slope, we can use the formula: We can pick any 2 points, such as (20, 63) and (22, 69). We can note that;

The y-intercept is the corresponding y-value when x=0. To find this using the information that we have, we can use the linear equation and plug in one point, such as (20,63), for x and y, and the slope, 3, for b, and solve for the y-intercept, : The y-intercept would be at 3.

The weekly feed cost for David's rabbit is $2.20. The rabbit used in a study weighs nine pounds.

Using the equation ŷ = 0.5 + 0.16x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for David's rabbit? a.) $1.94 b.) $0.26 c.) $1.35 d.) $0.85  Recall that to get the residual, we take the actual value minus the predicted value.

If the actual weight of a rabbit is 9 lbs and the resulting feed cost is $2.20, we first need to determine the predicted cost. Using the regression line, we can say: The predicted feed cost would be $1.94.

The residual is then: The weekly feed cost for Dianna's iguana is $2.10. The iguana used in a study weighs 11 pounds.

Using the equation ŷ = 0.4 + 0.15x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for Dianna's iguana? a.) $2.05 b.) $0.05 c.) $1.38 d.) $0.72  Recall that to get the residual, we take the actual value minus the predicted value.

If the actual weight of a iguana is 11 lbs and the resulting feed cost is $2.10, we first need to determine the predicted cost. Using the regression line, we can say: The predicted cost is $2.05.

The residual is then: The weekly feed cost for Dean's domestic shorthair cat is $2. The cat used in a study weighs 10 pounds.

Using the equation ŷ = 0.3 + 0.12x for the regression line of weekly food cost on weight (weight is explanatory), what is the residual for Dean's domestic shorthair cat? a.) $0.54 b.) $1.50 c.) $0.50 d.) $1.46  Recall that to get the residual, we take the actual value minus the predicted value.

If the actual weight of a cat is 10 lbs and the resulting feed cost is $2, we first need to determine the predicted cost. Using the regression line, we can say: The predicted cost is $1.50.

The residual is then: Why do we square the residuals when using the least-squares line method to find the line of best fit? a.)

We don't square the residuals when using the least-square method. b.)

It cancels out the effect of having negative and positive residuals. c.)

It amplifies the effect of having negative and positive residuals. d.)

Squaring the residuals makes it easier to identify smaller residuals.  We recall that in the least squares line, values will lie above and below the line of best fit. So when calculating the residuals, if we didn't square them, the sum of the residuals would be zero, canceling each other out.

Which of the following statements is true? a.)

The least-squares line is the process of minimizing the difference of the squared residuals. b.)

The least-squares line is the process of minimizing the product of the squared residuals. c.)

The least-squares line is the process of minimizing the quotient of the squared residuals. d.)

The least-squares line is the process of minimizing the sum of the squared residuals.

 We call a regression line the least squares line, because it is the line that minimizes the sum of all the squared residuals from the data.

Correct Go to the Next Concept Which of the following statements is FALSE? a.)

Squaring the residuals cancels the effects of positive and negative residuals. b.)

The difference of the squared residuals is used to calculate the least-squares line. c.)

The least-squares line is the most common way to find the line of best fit. d.)

The least-squares line should minimize residuals.  The difference of the squared residuals is not how we calculate the least squares line. We use the means of x and y, the standard deviations of x and y, and the correlation between x and y to get the intercept and slope. The least squares line is the the line that minimizes the sum of the squared residuals however.

The following table shows the relationship between the weight (in pounds) and the weekly feed cost (in dollars) for five pets.

Weight is the explanatory variable and has a mean of 24.5 and a standard deviation of 25.44.

Weekly feed cost is the response variable and has a mean of 7.6 and a standard deviation of 2.97.

The correlation was found to be 0.879.

Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. a.) slope = -0.10 y-intercept = 10.05 b.) slope = 7.53 y-intercept = 32.73 c.) slope = -7.53 y-intercept = 4.27 d.) slope = 0.10 y-intercept = 5.15  For a least-squares line, the slope will be equal to: To get the y-intercept, we use the formula:

The following table shows the relationship between the weight (in hundreds of pounds) and the miles per gallon (MPG) for five cars.

Weight is the explanatory variable and has a mean of 12.8 and a standard deviation of 6.02.

Miles per gallon is the response variable and has a mean of 19.8 and a standard deviation of 9.15.

The correlation was found to be -0.959.

Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. a.) slope = 0.63 y-intercept = 25.27 b.) slope = -1.46 y-intercept = 38.49 c.) slope = -0.63 y-intercept = 27.86 d.) slope = 1.46 y-intercept = 14.71  For a least-squares line, the slope will be equal to: To get the y-intercept, we use the formula: he following table shows the relationship between weight and calories burned per minute for five people.

Weight is the explanatory variable and has a mean of 149.4 and a standard deviation of 29.51.

Calories burned per minute is the response variable and has a mean of 9.65 and a standard deviation of 1.64.

The correlation was found to be 0.944.

Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place. a.) slope = -0.05 y-intercept = 17.12 b.)

slope = 16.99 y-intercept = 14.55 c.) slope = 16.99 y-intercept = 8.23 d.) slope = 0.05 y-intercept = 2.18  For a least-squares line, the slope will be equal to: To get the y-intercept, we use the formula: Robert enters data for weight (in pounds) and calories burned per minute into a statistics software package and finds a regression equation of ŷ = 2.2 + 0.05x, where weight is the explanatory variable.

Based on this information, select the conclusion about weight and calories burned per minute that is TRUE. a.)

For each additional pound of weight, calories burned per minute increases by 2.2 calories. b.)

For each additional pound of weight, calories burned per minute decreases by 0.05 calories. c.)

For each additional pound of weight, calories burned per minute stays relatively the same. d.)

For each additional pound of weight, calories burned per minute increases by 0.05 calories.  Recall that the slope for a linear equation is how much the outcome, y, changes for a one-unit change in x. So a slope of 0.05 implies every time weight increases by one pound, calories burned per minute increases by 0.05.

Sam enters data for weight (in pounds) and weekly food cost (in dollars) of pets into a statistics software package and finds a regression equation of ŷ = 0.3 + 0.12x, where weight is the explanatory variable.

Based on this information, select Sam's conclusion about food weight and costs that is TRUE. a.)

For each additional pound of weight, weekly food costs stays relatively the same. b.)

For each additional pound of weight, weekly food costs decreases by 12 cents. c.)

For each additional pound of weight, weekly food costs increases by 30 cents. d.)

For each additional pound of weight, weekly food costs increases by 12 cents.  Recall that the slope for a linear equation is how much the outcome, y, changes for a one-unit change in x. So a slope of 0.12 implies every time weight increases by one pound, fBlake enters data for weight (in hundreds of pounds) and miles per gallon of cars into a statistics

software package and finds a regression equation of ŷ = 38.5 - 1.4x, where weight is the explanatory variable.

Based on this information, select Blake's conclusion about weight and miles per gallon that is TRUE. a.)

For each additional one hundred pounds of weight, miles per gallon increases by 1.4 miles. b.)

For each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles. c.)

For each additional one hundred pounds of weight, miles per gallon decreases by 38.5 miles. d.)

For each additional one pound of weight, miles per gallon stays relatively the same.  Recall that the slope for a linear equation is how much the outcome, y, changes for a one-unit change in x. So a slope of -1.4 implies every time weight increases by one (hundred), mpg drops by 1.4. ood costs increase by $0.ght is the explanatory variab Which of the following situations describes a multiple regression? a.)

Using the motivational level and the amount of social support to predict the job performance and IQ scores of an individual. b.)

Using the motivation level, the amount of social support, and IQ scores to predict the job performance of an individual. c.)

Using IQ scores to predict the job performance of an individual. d.)

Using job performance to predict the motivational level and IQ scores of an individual.  Recall a multiple regression implies there are multiple explanatory variables used to predict a particular outcome. So using 3 variables (motivation, social support and IQ) to predict one response variable (job performance) illustrates that.

Which of the following situations describes a multiple regression? a.)

Using the IQ score to predict the body height and body weight of an individual. b.)

Using the brain volume, the body height, and the body weight to predict IQ score of an individual. c.)

Using the body height and body weight to predict IQ score and brain volume of an individual. d.)

Using the brain volume to predict the IQ score of an individual.  Recall a multiple regression implies there are multiple explanatory variables used to predict some outcome. So using 3 variables (brain volume, height and body weight) to predict one response variable (IQ score) illustrates that.

Which of the following situations describes a multiple regression? a.)

Using the average salary of a homeowner and the number of bedrooms to predict the listing price and square footage of a home. b.)

Using the average salary of a homeowner, the number of bedrooms, and the square footage to predict the listing price of a home. c.)

Using the square footage to predict the listing price of a home. d.)

Using the listing price of a home to predict the annual salary of a homeowner, the number of bedrooms, and the square footage.  Recall a multiple regression implies there are multiple explanatory variables used to predict some outcome. So using 3 variables, (salary of homeowner, square feet, and number of bedrooms) to predict one response variable (listing price of a home) illustrates that By observing a set of data values, Thomas used a calculator for the weight (in pounds) and predicted the number of calories burned per minute to get an equation for the least-squares line: ŷ = 2.2 + 0.05x.

Based on the information gathered by Thomas, select the statement that is TRUE. a.)

A person weighing 125 pounds can burn 8.3 calories per minute. b.)

A person weighing 173 pounds can burn 10.7 calories per minute. c.)

A person weighing 134 pounds can burn 8.9 calories per minute. d.)

A person weighing 149 pounds can burn 9.8 calories per minute.  In order to get the prediction, we simply plug in the value for the explanatory variable into our estimated regression equation. So if we plug x = weight = 134 into the least-squares line, then we get: A person weighing 134 pounds can burn 8.9 calories per minute.

By observing a set of data values, Tasha used a calculator for the tire diameter at the tread and circumference data and got an equation for the least-squares line: ŷ = 0.1 + 3.1x.

Based on this information, select the statement that is TRUE. a.)

A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches. b.)

A tire with a 28-inch diameter at the tread will have a circumference of 99.3 inches. c.)

A tire with a 35-inch diameter at the tread will have a circumference of 124.1 inches. d.)

A tire with a 32-inch diameter at the tread will have a circumference of 86.9 inches.  In order to get the prediction, we simply plug in the value for the explanatory variable into our estimated regression equation. So if we plug x = diameter = 30 into the least-squares line, then we get: A tire with a 30-inch diameter at the tread will have a circumference of 93.1 inches.

Correct By observing a set of data values, Tina used a calculator for the engine speed and predicted horsepower to get an equation for the least-squares line: ŷ = 10 + 30x.

Based on the data that Tina collected, select the statement that is TRUE. a.)

The horsepower associated with an engine speed of 0.5 rpm would be 40 hp. b.)

The horsepower associated with an engine speed of 1.5 rpm would be 70 hp. c.)

The horsepower associated with an engine speed of 2.5 rpm would be 85 hp. d.)

The horsepower associated with an engine speed of 3.5 rpm would be 110 hp.  In order to get the prediction, we simply plug in the value for the explanatory variable into our estimated regression equation. So if we plug x = rpm = 2.5 into the least-squares line equation, then: A horsepower with an engine speed o 2.5 rpm would be 85 hp.

A local shop's weekly sales of ice cream and sunglasses are presented in the table.

Ice Cream Sunglasses Monday 3 5 Tuesday 4 6 Wednesday 5 7 Thursday 7 9 Friday 8 9 The calculation for the correlation, r, for this set of five data points is __________. Answer choices are rounded to the hundredths place.  0.77   b.)  0.88

  c.)  0.98   d.)  0.94 