Given a scenario and a dataset (see attached excel file), you are required to ru

Question

Given a scenario and a dataset (see attached excel file), you are required to run regression of the dataset, and present your results in a report. In your report, you should include an introduction which describes the case, the study purpose and the demand function as an equation which you would like to estimate and regression results in table. Following the introduction, you need to include the four steps to interpret the regression results:

Step 1: interpret coefficient signs and magnitudes

Step 2: compute elasticity coefficient and interpret the elasticities. Please use data of Store 1 to compute elasticities, as shown below:

Sales (1000)

Price ($)

Advertising ($1000)

Price X ($)

Income ($1000)

3.5

80

3.3

61

4.9

Step 3: Statistical evaluation of regression results

Step 4: Analyze managerial decisions

Store Sales (1000) Price ($) Advertising ($1000) Price X ($) Income ($1000) 1 3.5 80 3.3 61 4.9 2 4.6 60 3.3 49 5.4 3 3.5 78 3 49 4.8 4 4.3 65 4.5 54 5.1 5 3.5 70 3 53 4.5 6 3.8 75 4 49 4.3 7 4.3 45 3 62 5.6 8 4.7 55 3.7 55 5.8 9 4.5 70 3.5 63 5.7 10 4.9 55 4 59 5.5 11 3.4 75 3.5 49 4.9 12 3 75 3.2 56 4.3 13 4.4 59 4 53 5.9 14 4.5 56 3.5 61 6.1 15 3 80 2.7 53 4.8 16 3.5 78 3 54 4.7 17 4.2 75 3.5 62 5.7 18 4 70 3.5 49 5.3 19 4.6 60 3.7 54 5.9

Explanation / Answer

The regression results are as follows :-

Step 1, 3 and 4 :- Interpretation of results :-
For every 1 $ increase in price the mean sales decreases by 0.00457*1000 = 4.57 units.
For every 1000$ spent on advertising the mean sales increase by 0.221457*1000 = 221.457 units
For every 1 $ incease in Price X the mean sales decreases by 0.01062*1000 = 10.62 units.
For every 1000$ increase in income the mean sales increases by 0.751486*1000 = 751.486 units.

Step 2:-
Elasticity = dQ/dp * P/Q
               ( Sorry, do not know how to find elasticity here )

SUMMARY OUTPUT Regression Statistics Multiple R 0.812405 R Square 0.660002 Adjusted R Square 0.562859 Standard Error 0.393237 Observations 19 ANOVA df SS MS F Significance F Regression 4 4.202473 1.050618 6.794163 0.002951726 Residual 14 2.164896 0.154635 Total 18 6.367368 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 0.153082 2.167122 0.070638 0.944685 -4.494933773 4.801097 -4.49493 4.801097 Price($) -0.00457 0.012658 -0.36075 0.723675 -0.031715893 0.022583 -0.03172 0.022583 Advertising ($1000) 0.221457 0.224134 0.988056 0.339895 -0.259262267 0.702176 -0.25926 0.702176 Price X($) -0.01062 0.021193 -0.50122 0.624005 -0.056076673 0.034832 -0.05608 0.034832 Income($1000) 0.751486 0.248316 3.026324 0.009066 0.218900185 1.284072 0.2189 1.284072

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