A company has recorded data on the weekly sales for its prod

A company has recorded data on the weekly sales for its product (y), the unit price of the competitor\'s product (x_1), and advertising expenditures (x_2). The data resulting from a random sample of 7 weeks follows. Use Excel\'s Regression Tool to answer the following questions. What is the estimated regression equation? Determine whether the model is significant overall. Use alpha = 0.10. Determine if price is significantly related to sales. Use alpha = 0.10. Determine if advertising is significantly related to sales. Use alpha = 0.10. Find and interpret the multiple coefficient of determination.

Solution

Sol)

The multiple Regresssion equation is

Y=a+bx1+cx2

where y is sales and x1 is price , x2 is advertise ment

From excel

A) The estimated regression equation is

y=3.598 +41.32(sales) + 0.0132 (Adv)

B) From above analysis

F cal=6.71

and P value=0.05 and alpha=0.10

Since P< alpha, Hence The model is significant

C)

price:

P value=0.036 and alpha=0.10

Since P< alpha, Hence the price is significantly related to sales

D)

Advertising

P value=0.967 and alpha=0.10

Since P> alpha, Hence the advertising is not significantly related to sales

E) Coefficient of determination

R² =0.7705

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.877814
R Square	0.770558
Adjusted R Square	0.655837
Standard Error	1.83741
Observations	7
ANOVA
	df	SS	MS	F	Significance F
Regression	2	45.35284	22.67642223	6.716801	0.052644
Residual	4	13.5043	3.376074598
Total	6	58.85714
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 90.0%	Upper 90.0%
Intercept	3.597615	4.052244	0.887808146	0.424805	-7.65322	14.84845	-5.04115	12.23638
price	41.32002	13.33736	3.098065458	0.036289	4.289567	78.35048	12.88681	69.75324
adv	0.013242	0.327592	0.040421723	0.969694	-0.8963	0.922782	-0.68513	0.711617