Question

1. The following output was obtained from a regression analysis of the dependent variable Sales volume and an independent variable “location distance from the downtown branch.      

ANOVA
	df	SS	MS	F
Regression	2	552.137	267.069	24.235
Residual	10	110.22	11.02
Total	12	662.357
	Coefficients	Standard Error	t Stat	P-value
Intercept	-38.623	3.630	12.569	0.000
Location distance	0.309	0.016	6.552	0.000

1. Calculate and interpret the correlation coefficient. What does it tell us? (1.5 marks)

2. Calculate and interpret the coefficient of determination. (1.5 marks)

3. What is the estimated regression equation? (1 mark)

4. Calculate the estimated sales volume if we open up a store which is 15.6 km away from the central branch in downtown.

Answer 1

Answer: The following output was obtained from a regression analysis of the dependent variable Sales volume and an independent variable "location distance from the downtown branch.

Solution:

a) Calculate and interpret the correlation coefficient. What does it tell us?

Correlation coefficient, r = √(Regression SS/Total SS)

Correlation coefficient = √552.137/662.357

Correlation coefficient, r = 0.9130.

Interpretation:

There is a strong positive linear relationship between dependent variable Sales volume and independent variable location distance from the downtown branch.

b) Calculate and interpret the coefficient of determination.

Coefficient of determination r^2 = (0.9130)^2

Coefficient of determination, r^2 = 0.8336

Interpretation:

Coefficient of determination explained 83.36% of variation in Sales volume data on location distance from the downtown branch.

c) What is the estimated regression equation?

Y = β_{​​​​​​0} + β₁​​​​​X

Where, Y - Sales volume

X - Location distance from downtown branch.

Y = - 38.623 + 0.309X.

d)Calculate the estimated sales volume if we open up a store which is 15.6 km away from the central branch in downtown.

When X = 15.6

Y = - 38.623 + 0.309X

Y = - 38.623 + 0.309(15.6)

Y = - 33.8026

Therefore, the estimated sales volume if we open up a store 15.6 km away from the central branch in downtown is -33.8026.