Question

In: Statistics and Probability

A chain store corporation wants study the effects of price decrease (x1, in %) and advertising expenditure increase (x2) on sales volume (y).

 

A chain store corporation wants study the effects of price decrease (x1, in %) and advertising expenditure increase (x2) on sales volume (y). The corporation imposes different levels of price decrease and advertising expenditure increase on its product in stores in eight different districts of the country and measures the changes in sales volume over the next three months. A multiple regression model is used and the following output is extracted from the computer software.

ANOVA

  df SS MS F
Regression ? ? ? ?
Residual ? ? ?  
Total ? ?    
  Coefficients Standard Error    
Intercept 0.1285 0.9018    
x1 0.0471 0.1213    
x2 0.4141 0.1742    
         

i. Write down the fitted multiple linear regression equation. [1 mark]

ii. Complete the above ANOVA table for the multiple linear regr P ession if y = 42, Py 2 = 256 and only 7.66% of variation in sales volume cannot be explained by price decrease and advertising expenditure. [3 marks]

iii. Test the overall significance of the fitted equation in part i. at 1% level of significance. [3 marks]

iv. Test the significance of price decrease in affecting the sales volume at 1% level of significance

Solutions

Expert Solution


Related Solutions

A department store investigated the effects of advertising expenditure on the weekly sales for its men's...
A department store investigated the effects of advertising expenditure on the weekly sales for its men's wear, children's wear, and women's wear departments. Five weeks were randomly selected for each department to be used in the analysis (this makes 15 weeks in total, ?n). The variables are as follows: ?y = weekly sales ?1x1 = advertising expenditure ?2x2 = 1 if it is the children's wear department and a 0 otherwise ?3x3 = 1 if it is the women's wear...
In a study relating consumption expenditure (Y) on income (X2) and wealth (X3) based on 10...
In a study relating consumption expenditure (Y) on income (X2) and wealth (X3) based on 10 observations , the following equation was obtained Yhat = 24.337 + 0.08764X2 - 0.0349X3      SE   (6.2801)    (0.31438)   (0.0301)        t    (3.875)      (2.7726)     (-1.1595)                i) In your opinion, what type of problem takes in this result? Explain it ii)   What are the practical consequences of this problem? iii) What are the theoretical of this problem iv) How to detect this problem? v)In your judgement,...
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the...
A regression analysis relating a company’s sales, their advertising expenditure, price, and time resulted in the following. Regression Statistics Multiple R 0.8800 R Square 0.7744 Adjusted R Square 0.7560 Standard Error 232.29 Observations 25 ANOVA df SS MS F Significance F Regression 3 53184931.86 17728310.62 328.56 0.0000 Residual 21 1133108.30 53957.54 Total 24 54318040.16 Coefficients Standard Error t Stat P-value Intercept 927.23 1229.86 0.75 0.4593 Advertising (X1) 1.02 3.09 0.33 0.7450 Price (X2) 15.61 5.62 2.78 0.0112 Time (X3) 170.53...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Advertising (x) Sales (y) 400,000 6,000,000 500,000 7,200,000 500,000 8,000,000 660,000 7,500,000 790,000 8,900.000 540,000 8,100,000 420,000 5,900.000 380,000 4,000,000 If the company's advertising expenditure is $315,000, what are the predicted sales? If the company wanted $9,500,000 in sales, what should the advertising budget be?
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. Sales in Millions of Dollars Advertising in ($10,000) 11 32 16 33 18 35 17 34 16 36 19 37 19 39 24 42 a. Which variable is the dependent variable? b. Using the Excel spreadsheet, run the least squares model and write the summary output here. c. If the company's advertising expenditure is $400,000, what are the predicted sales? Give...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years. (Y) Sales in Millions of Dollars (X) Advertising in ($10,000) 14 32 15 33 18 35 17 34 16 36 a. Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. b. Use the method of least squares to compute an estimated regression line between sales and advertising. c. If the...
The following data represent a company’s yearly sales volume and its advertising expenditure over a period...
The following data represent a company’s yearly sales volume and its advertising expenditure over a period of 8 years. Year                            Sales (Y)                                  Advertising (X) 1989                            15                                                        32 1990                            16                                                        33 1991                            18                                                        35 1992                            17                                                        34 1993                            16                                                        36 1994                            19                                                        37 1995                            19                                                        39 1996                            24                                                        42 Develop a scatter diagram of sales versus advertising Use the method of least squares to compute an estimated regression line between sales and advertising. If the company’s advertising expenditure is $40, what...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.                                                 (Y)                                          (X)         Sales in millions                     Advertising in ($10,000)                                                 15                                            32                                                 16                                            33                                                 18                                            35                                                 17                                            34                                                 16                                            36 (a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising. (b) Use the method of least squares to compute an estimated regression line between sales and...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 8 years.              Sales (Millions) Advertising ($10,000) 15 32 16 33 18 35 17 34 16 36 19 37 19 39 24 42 To make sure the Excel regression package is installed. Click “Tools”, à“Add-Ins” àchoose “Analysis Toolpak” and click “OK”. To use the Excel regression package,                                                      Click “Tools”, à“Data Analysis” and click “Regression”.                                                                          a.   Use the method of least squares to compute...
The following data represent a company's yearly sales volume and its advertising expenditure over a period...
The following data represent a company's yearly sales volume and its advertising expenditure over a period of 5 years. (Y) Sales in Millions of Dollars 15 16 18 17 16 (X) Advertising in ($10,000) 32 33 35 34 36 (a) Compute the coefficient of determination for the estimated regression equation you got in the previous in-class problem. (b) Interpret the meaning of the value of the coefficient of determination that you found in (a). Be very specific. (c) Perform a...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT