Question 1. When Blanchard shows your previous regression to Tyler to make his case for c-store advertising, she flat-out rejects your analysis. She argues that you omitted an important variable, namely the average high temperature in a week. “As we all know,” she says, “we advertise more during the warm weather periods in Marseille. So the seemingly large effect of advertising in your regression is not truly due to the positive impact of advertising but instead reflects the impact good weather has on driving and on the demand for gas and convenience items. To address Tyler’s criticism include temperature in your previous regression.

4.a)Compare your new regression (with three independent variables) to your previous regression. Does Tyler’s criticism appear to be justified? Explain.

The comparison between the two regression models, first using one independent variable and second using three independent variable the results shows that the significance level of these two are different as Fuel volume is not effecting the sales value, but advertising through TV and Radio are affecting the sales value having the significant level of around 0.9747. Tyler’s criticism is justified using the regression model as €1 of sales is generated using the advertising from TV and Radio.

4.b) Drop all variables from your regression that do not meet Tyler’s desired level of significance. Based on the resulting regression, does advertising appear to be profitable? Provide an estimate of the net impact of c-store advertising.

The advertising is profitable as it gives positive sales revenue given below in the Table 4:

Table 4:

RESIDUAL OUTPUT |
PROBABILITY OUTPUT |
||||

Observation |
Predicted Sales |
Residuals |
Standard Residuals |
Percentile |
Sales |

1 |
25026.00213 |
-162.0021327 |
-0.14613659 |
5 |
23688 |

2 |
25026.00213 |
-1217.002133 |
-1.09781605 |
15 |
23809 |

3 |
25053.95554 |
-577.9555409 |
-0.52135395 |
25 |
23922 |

4 |
25053.95554 |
225.0444591 |
0.203004919 |
35 |
24421 |

5 |
25053.95554 |
1209.044459 |
1.090637704 |
45 |
24476 |

6 |
24858.08165 |
-1170.081651 |
-1.055490686 |
55 |
24864 |

7 |
24821.37704 |
-899.3770388 |
-0.811297303 |
65 |
25279 |

8 |
24978.95586 |
-557.9558605 |
-0.503312921 |
75 |
26197 |

9 |
24978.95586 |
1218.04414 |
1.098756008 |
85 |
26263 |

10 |
24832.7587 |
1932.241299 |
1.743008868 |
95 |
26765 |

From the above table the advertising contributing into the sales with the significant level of around 0.710 and in the first week of advertising, the predicted sales would be around 25026 that is comprised of the advertising that is contributing the 8342.

4.c)What needs to be true in order for the coefficients in your regression for c-store advertising to be profitable? Can you prove that advertising is profitable?

In order to get the profit using advertising for the sales of c-stores, the coefficients of the TV advertising must be positive so that advertising would help in generation of more revenues. Advertising is profitable as it aware the knowledge about the products available in the c-stores and also it attracts the customers towards the c-store as c-store is about providing all the products.

Question 2. When you show your latest regression to Blanchard, he becomes rather concerned that you have not accounted for many other factors that could affect c-store sales. Surely Tyler will sooner or later complain about that fact. He asks you to extend your analysis.

To address Blanchard’s concerns include all other variables (excluding the week of the year).

Answer:

The regression analysis using all the given data for satisfying the Blanchard’s concern the results shown in Excel sheet Q-5.

5-a) Drop again all variables from your regression that do not meet Tyler’s desired level of significance. Report your final regression equation.

In this equation b1x1 representing the TV, b2x2 representing the Radio, b3x3 representing the Fuel volume, b4x4 representing the fuel prices, b5x5 is representing the temperature, b6x6 representing the average annual precipitation, b7x7 representing the holidays, and b8x8 representing the variable customer’s visit, are independent variable in the equation and Y variable representing Sales variable is dependent variable in the equation.

5-b) Carefully interpret the meaning of each slope coefficient in the context of this case. Comment on the signs of the coefficients. Do you observe any seemingly unintuitive signs? Provide possible explanations for any such signs.

In this, the regression model is showing that the slope of the regression model is 9290 which represents that if any changes occurs in the TV, it would change the Y variable which is sales. With respect to all the independent variables used in this model any changes would affect the sales either negative or positive.

5-c) Provide a 95 percent interval for the increase in c-store sales if TV GRPs rise by 5 rating points.

If TV GRP rise through 5 rating points it would change the sales and affect the sales to drop by the 92.122 and at this interval the significance level would be 95 percent.................................

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