Profits Use the given Sample data for profits made by super markets and follow t
ID: 3259649 • Letter: P
Question
Profits
Use the given Sample data for profits made by super markets and follow the instructions below:
Instructions
1. Run a regression using the given data. (With Profit as the dependent variable and Store size as the independent variable)
2. Compare the results of question (1) with another regression equation obtained by regressing the Profit on the variables : Food Sales and Non food sales.
3. Which of the models do you prefer? Why?
4. Interpret your results for (1) and (2).
***ALSO, PLEASE ANSWER THE QUESTION BELOW***
**Remember that the results section should include hypothesis testing for a t-test about each slope coefficient and an F-test for the overall regression model. Use = 0.05 for both the T test and F test
EXAMPLE:
For the t-test, it is written like this:
H0: B1= 0
Ha: B1=/ 0
Note:
You have to decide whether to use one-tail or two-tail test
You need to follow chapter 9 materials and declare your alternative hypothesis in each case very well
F-test:
H0: B1= B2= B3= 0
Ha: B1=/ B2=/ B3 =/ 0, or all three are =/ 0
Note: mention what is used in your hypothesis testing.
Supermarket Number X1 X2 X3 Y 1 305 35 35 20 2 130 98 22 15 3 189 83 27 17 4 175 76 16 9 5 101 93 28 16 6 269 77 46 27 7 421 44 56 35 8 195 57 12 7 9 282 31 40 22 10 203 92 32 23Explanation / Answer
The regression output as obtained from excel by taking independent variables as Food Sales (tens of thousands of dollars), Non-food Sales (tens of thousands of dollars), and Store Size (thousands of square feet). Regression equation is given as
Price = -10.17 + 0.02*food_sales + 0.09*non_food_sales + 0.52*store_size
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.992399
R Square
0.984855
Adjusted R Square
0.977283
Standard Error
1.249868
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
3
609.527
203.1757
130.0599
7.56E-06
Residual
6
9.373017
1.562169
Total
9
618.9
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-10.1702
3.473129
-2.92827
0.026346
-18.6687
-1.6718
-18.6687
-1.6718
Food Sales
0.027038
0.012041
2.245505
0.065847
-0.00243
0.056501
-0.00243
0.056501
Non food Sales
0.097052
0.030147
3.219291
0.018153
0.023285
0.17082
0.023285
0.17082
Store Size
0.524675
0.059158
8.869011
0.000114
0.37992
0.66943
0.37992
0.66943
The regression output as obtained from excel by taking independent variables as Non-food Sales (tens of thousands of dollars), and Store Size (thousands of square feet). Regression equation is given as
Price = -3.75 + 0.04*non_food_sales + 0.6338*store_size
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.985966
R Square
0.972128
Adjusted R Square
0.964165
Standard Error
1.569801
Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
2
601.6501
300.825
122.0744
3.61E-06
Residual
7
17.24993
2.464276
Total
9
618.9
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-3.75836
2.483252
-1.51348
0.173924
-9.63032
2.1136
-9.63032
2.1136
Non food Sales
0.043114
0.02288
1.884348
0.101515
-0.01099
0.097216
-0.01099
0.097216
Store Size
0.633782
0.042384
14.95321
1.44E-06
0.533559
0.734005
0.533559
0.734005
Results
Ho1: model with food sales is not significant versus h11: model with food sales is significant. With F=130.05 and p-value < 0.05 (alpha), I reject ho at 5% level of significance and conclude that model with food sales is significant.
Ho2: model without food sales is not significant versus h12: model without food sales is significant. With F=122.07 and p-value < 0.05 (alpha), I reject ho at 5% level of significance and conclude that model without food sales is significant.
Coefficient of determination for model with food sales has R12 = 0.9848 implies that 98.48% of the variation of prices around its mean is explained by the independent variables Food Sales (tens of thousands of dollars), Non-food Sales (tens of thousands of dollars), and Store Size (thousands of square feet). Thus, the fitted line is a good fit to the data and the model seems to be accurate. But case for model without food sales, Coefficient of determination R22 = .9721, implies that 98.48% of the variation of prices around its mean is explained by the independent variables Non-food Sales (tens of thousands of dollars), and Store Size (thousands of square feet). Since, there is not much difference in the percentage of variation in the dependent variable which is explained by the independent variables, I prefer model without food sales as it has less number of independent variables.
For model with food sales, consider the hypothesis, Ho1: 1=0, 1 is not significant v/s H11: 10, 1 is significant. With p-value is greater than alpha (0.05), I fail to reject ho at 5% level of significance and conclude that 1 is not significant. hence, food sales should be excluded from the model.
For model with food sales, Ho2: 2=0, 2 is not significant v/s H12: 20, 2 is significant. With p-value is less than alpha (0.05), I reject ho at 5% level of significance and conclude that 2 is significant.
For model with food sales, Ho3: 3=0, 3 is not significant v/s H13: 30, 3 is significant. With p-value is less than alpha (0.05), I reject ho at 5% level of significance and conclude that 3 is significant.
For model without food sales, consider the hypothesis, Ho1: 1=0, 1 is not significant v/s H11: 10, 1 is significant. With p-value is less than alpha (0.05), I reject ho at 5% level of significance and conclude that 1 is significant.
For model without food sales, Ho2: 2=0, 2 is not significant v/s H12: 20, 2 is significant. With p-value is less than alpha (0.05), I reject ho at 5% level of significance and conclude that 2 is significant.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.992399
R Square
0.984855
Adjusted R Square
0.977283
Standard Error
1.249868
Observations
10
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