Question

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(b₁) 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 = 0.01. Please show all the relevant calculations.

(10 points)

H₀ : β₁ = 0

H₁ : β₁ ≠ 0

3) Perform the test of hypothesis (F-test) on the following, and state your statistical decision. Use α = 0.01. Please show all the relevant calculations.  

(10 points)

H₀ : β₁ = 0

H₁ : β₁ ≠ 0

4) What is the coefficient of determination (r²) 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)?

Answer 1

Regression Statistics
Multiple R	0.98516189
R Square	0.97054396
Adjusted R Square	0.96072527
Standard Error of the Estimate	6.03
Observations	8
ANOVA
	df	SS	MS	F
Regression	1	7181.54	7181.54	197.6933382
Residual/ Error	6	217.96	36.3266667
Total	7	7399.5
	Coefficients	SE Coef/ Standard Error	t-value	p-value
Intercept	96.27	5.84	16.484589	3.17637E-06
Promo Exp(X)/ Estimated slope	13.02	0.93	14	8.28223E-06

1) What is the slope(b₁) and what is its statistical interpretation ? (10 points)

The slope is 13.02.

For every additional promo expenditure, demand will increase by 13.02.

2) Perform the test of hypothesis ( t-test) on the following, and state your statistical decision. Use α = 0.01. Please show all the relevant calculations.

(10 points)

H₀ : β₁ = 0

H₁ : β₁ ≠ 0

The p-value from the output is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that β₁ ≠ 0.

3) Perform the test of hypothesis (F-test) on the following, and state your statistical decision. Use α = 0.01. Please show all the relevant calculations.  

(10 points)

H₀ : β₁ = 0

H₁ : β₁ ≠ 0

The p-value from the output is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that β₁ ≠ 0.

4) What is the coefficient of determination (r²) i.e., percentage of variability in Demand explained by the independent variable Promo Expenditure? Please show all the relevant calculations. (10 points)

0.97054396

5) What is the value of the standard error of the estimate (S_YX) in dollars (10 points)?

6.03