Linear Regression Formula Linear Regression Formula Regression Definition : A regression is a statistical analysis assessing the association between two variables. It is used to find the relationship between two variables. Regression Formula : Regression Equation(y) = a + bx Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) Intercept(a) = (ΣY - b(ΣX)) / N where
x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores Know More About Graphing a Circle
Math.Tutorvista.com
Page No. :- 1/5
Step 1: Count the number of values. N=5 Step 2: Find XY, X2 Step 3: Find ΣX, ΣY, ΣXY, ΣX2. ΣX = 311 ΣY = 18.6 ΣXY = 1159.7 ΣX2 = 19359 Step 4: Substitute in the above slope formula given. Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) = ((5)*(1159.7)-(311)*(18.6))/((5)*(19359)-(311)2) = (5798.5 - 5784.6)/(96795 - 96721) = 13.9/74 = 0.19 Step 5: Now, again substitute in the above intercept formula given. Intercept(a) = (ΣY - b(ΣX)) / N = (18.6 - 0.19(311))/5 = (18.6 - 59.09)/5 = -40.49/5 = -8.098 Step 6: Then substitute these values in regression equation formula Regression Equation(y) = a + bx = -8.098 + 0.19x. Suppose if we want to know the approximate y value for the variable x = 64. Then we can substitute the value in the above equation. Learn More Circle Graph Maker Math.Tutorvista.com
Page No. :- 2/5
Correlation Formula Correlation Formula Correlation Co-efficient Definition : A measure of the strength of linear association between two variables. Correlation will always between -1.0 and +1.0. If the correlation is positive, we have a positive relationship. If it is negative, the relationship is negative. Formula : Correlation Co-efficient : Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])] where N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores ΣY2 = Sum of square Second Scores Step 3: Find ΣX, ΣY, ΣXY, ΣX2, ΣY2.
Math.Tutorvista.com
Page No. :- 3/5
ΣX = 311 ΣY = 18.6 ΣXY = 1159.7 ΣX2 = 19359 ΣY2 = 69.82 Step 4: Now, Substitute in the above formula given. Correlation(r) =[ NΣXY - (ΣX)(ΣY) / Sqrt([NΣX2 - (ΣX)2][NΣY2 - (ΣY)2])] = ((5)*(1159.7)-(311)*(18.6))/sqrt([(5)*(19359)-(311)2]*[(5)*(69.82)-(18.6)2]) = (5798.5 - 5784.6)/sqrt([96795 - 96721]*[349.1 - 345.96]) = 13.9/sqrt(74*3.14) = 13.9/sqrt(232.36) = 13.9/15.24336 = 0.9119 This example will guide you to find the relationship between two variables by calculating the Correlation Co-efficient from the above steps. The square of the correlation coefficient, r², is a useful value in linear regression. This value represents the fraction of the variation in one variable that may be explained by the other variable. Thus, if a correlation of 0.8 is observed between two variables (say, height and weight, for example), then a linear regression model attempting to explain either variable in terms of the other variable will account for 64% of the variability in the data. The correlation coefficient also relates directly to the regression line Y = a + bX for any two variables, where . Because the least-squares regression line will always pass through the means of x and y, the regression line may be entirely described by the means, standard deviations, and correlation of the two variables under investigation. Read More About Lower Quartile
Math.Tutorvista.com
Page No. :- 4/5
Thank You
Math.TutorVista.com