A company has recorded data on the weekly sales for its product (y), the unit pr

Question

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 a = 0.10. Determine if price is significantly related to sales. Use a = 0.10. Determine if advertising is significantly related to sales. Use a = 0.10. Find and interpret the multiple coefficient of determination.

Explanation / Answer

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

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