A marketing manager in charge of a profit center for Max Department Stores Compa

Question

A marketing manager in charge of a profit center for Max Department Stores Company is interested in developing a multiple regression model to predict the marketing budget Y (in tens on thousands of dollars) allowed for a product from previous product sales X_1 (in tens of thousands of dollars) and the stage of the life cycle for the product X_2 The life cycle of the product is coded as growth = 0 and maturity =1. Data were collected for 20 products and are presented below. Run a regression analysis and answer the below quests. a. Find the multiple regression equation for y regressed on x_1 and x_2. Briefly interpret the equation. Find the predicted value for V given X_1 = 50 and X_2 = 1. t c. Find SST, SSR, SSE, n-k-1, MSR, and MSE, and present the results in an analysis of variance table. d. Find the value of the standard error of the estimate, sy12. Briefly interpret the results. e. Find the coefficient of multiple determination R-squared. Briefly interpret the results. f. Is multicollinearity a problem? Indicate why or why not. g. Test the overall significance of the that is, test H_o: b_1 = b_2 = 0 the a significant level of 05. h. Test each independent variable separately to see whether it contributes explanatory power to the regression equation over and above that provided by the other independent variable, that is test H_0: bj = 0 against H+a = 0. Use 05 for the level of significance.

Explanation / Answer

The below answer is solved through excel

1)

Budget = 2.217 + 0.071x1 + 3.545x2

b) Budget = 2.217+0.071*50+3.545 = 9.312

c)

d) From descriptive statistics Standard error of estimate y = 0.831

SUMMARY OUTPUT Regression Statistics Multiple R 0.942525 R Square 0.888354 Adjusted R Square 0.875219 Standard Error 0.831198 Observations 20 ANOVA df SS MS F Significance F Regression 2 93.45487 46.72743 67.63367 8.07E-09 Residual 17 11.74513 0.69089 Total 19 105.2 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.216647 0.737829 3.004284 0.007981 0.659965 3.773329 0.659965 3.773329 Sales 0.070974 0.015209 4.666742 0.000221 0.038887 0.103061 0.038887 0.103061 Life Cycle 3.544847 0.394042 8.996115 7.13E-08 2.713491 4.376203 2.713491 4.376203

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