Question B:
Consider the following MS Excel partial output for the independent variable monthly Promo Expenditure ‘X’ (in 100s of dollars) and the monthly Demand ‘Y’ for a product’ (in 1000s of dollars)
Regression Analysis: Demand (in thousands of $) versus Promo Exp (in hundreds of $)
SUMMARY OUTPUT | ||||
Regression Statistics | ||||
Multiple R | ||||
R Square | ||||
Adjusted R Square | ||||
Standard Error of the Estimate | 6.03 | |||
Observations | 8.00 | |||
ANOVA | ||||
df | SS | MS | F | |
Regression | 7181.54 | |||
Residual/ Error | ||||
Total | 7 | 7399.50 | ||
Coefficients | SE Coef/ Standard Error | |||
Intercept | 96.27 | 5.84 | ||
Promo Exp(X)/ Estimated slope | 13.02 | 0.93 |
Please answer the following questions based on the above Excel output
1) What is the slope(b_{1}) and what is its statistical interpretation ? (10 points)
2) Perform the test of hypothesis ( t-test) on the following, and state your statistical decision. Use α = 0.05. Please show all the relevant calculations.
(10 points)
H_{0} : β_{1} = 0
H_{1} : β_{1} ≠ 0
3) Perform the test of hypothesis (F-test) on the following, and state your statistical decision. Use α = 0.05. Please show all the relevant calculations.
(10 points)
H_{0} : β_{1} = 0
H_{1} : β_{1} ≠ 0
4) What is the coefficient of determination (r^{2}) i.e., percentage of variability in Demand explained by the independent variable Promo Expenditure? Please show all the relevant calculations. (10 points)
5) What is the value of the standard error of the estimate (S_{YX}) in dollars (10 points)?