Problem 3-26 The following data were collected during a study of consumer buying
ID: 396624 • Letter: P
Question
Problem 3-26 The following data were collected during a study of consumer buying 16 77 23 81 36 89 33 8611 55 92 44 94 31 84 1775 15 72 10 2682 26 92 37 87 b. Obtain e linear regression line for the data.(Round your intermediate calculations and final answers to 3 decimal places.) c. What percentage of the variation is explained by the regression line? (Do not round intermediate calculetions. Round your answer to the nearest whole percent. Omit the-%" sign in your response.) Approximately % of the variation in the dependent variable is explained by the independent variable. ation determined in part b to predict the expected velue of yfor xs 45 (Round your intermediate calculations and finel answers to 3 decimal places.)Explanation / Answer
Let the linear regression line :
Y = a + b.X
Where,
X ( independent variable )
Y ( Dependent variable )
A, b = Constants
We place all the values of x and y as provided in the problem in 2 adjacent columns in excel and apply the formula LINEST ( ) and apply the formula LINEST ( ) to determine values of A and B .
Accordingly values of A and B as follows :
A= 68.527
B = 0.519
Thus the regression line :
Y = 68.527 + 0.519.X
b. Linear regression line : Y = 68.527 + 0.519.X
Coefficient of determination ( r^2) expressed in percentage terms explains % of variation in dependent variable explained by independent variable.
Coefficient of determination = Correlation coefficient ^2
To determine correlation coefficient , we apply the formula CORREL ( ) on values of X and Y placed in adjacent columns in excel. Accordingly, we derive value of correlation coefficient as 0.8625
Therefore, coefficient of determination
= 0.8625 x 0.8625
= 0.7439
Therefore , percentage of variation in dependent variable as explained by independent variable = 0.7439 x 100 = 74.39%
c.ANSWER : 74.39%
Expected value of Y for X = 15
= 68.527 + 0.519 X 15
= 68.527 + 7.785
= 76.312
b. Linear regression line : Y = 68.527 + 0.519.X
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