Question

In: Statistics and Probability

On top of the its own price effect on sales, Mr. Wok is also interested how...

  1. On top of the its own price effect on sales, Mr. Wok is also interested how the sales will change as Competitor’s price changes.

Please use data in “Linear regressions with competitor price.xsls”

  • Estimate the coefficients with Mr. Work’s own price and its competitor
  • How do the two prices affect the Mr. Works’s sales?
Data
Market Sales Price
1 167 2.5
2 182 2.5
3 167 2.7
4 147 2.8
5 167 2.3
6 195 2.2
7 175 2.7
8 198 2.0
9 147 2.8
10 187 2.6
11 181 2.7
12 221 1.9
Market ID Sales Price   Competitor Price (Cprice)
1 228 2.2 2.2
2 216 2.7 2.9
3 223 2.4 2.4
4 207 2.9 2.6
5 216 2.8 2.4
6 247 2.2 2.5
7 233 2.0 2.2
8 249 2.3 2.7
9 239 2.1 2.4
10 209 2.7 2.4
11 214 2.8 2.4
12 236 2.6 3.0
13 218 2.6 2.1
14 191 2.9 2.2
15 223 2.6 3.0

Solutions

Expert Solution

In order to solve this question I used Excel.

Step.1 Enter data in excel sheet.

Step.2 Go to 'Data' menu ---> 'Data Analysis' ---> Select 'Regression'.

Step.3 New window will pop-up on screen. Refer following screen shot and enter information accordingly.

Excel output:

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.899159
R Square 0.808488
Adjusted R Square 0.776569
Standard Error 7.453419
Observations 15
ANOVA
df SS MS F Significance F
Regression 2 2814.292 1407.146 25.32959 4.93E-05
Residual 12 666.6414 55.55345
Total 14 3480.933
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 284.8645 22.03959 12.92513 2.11E-08 236.8444 332.8846
Price   -46.6048 6.807572 -6.84603 1.78E-05 -61.4372 -31.7724
Competitor Price (Cprice) 22.39825 6.962266 3.217092 0.007394 7.228775 37.56772

Estimated regression equation is,

Sales = 284.8645 - 46.6048 Price + 22.39825 Competitor price.

It means if Mr. Work's price is increased by 1 unit then his sale decreased by 46.6048 units.

And if  Competitor price increased by 1 unit then Mr. Work's sale increased by 22.39825 units.


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