An owner of an ice cream shop wants to determine the factors that affect ice cream sales in a day. Over 9 days, he calculates the Sales (in $100) of the shop, the high temperature that day (Temp), whether it was a Weekend (1 if it was weekend, 0 if it was a weekday), whether it was Rainy that day (1 if it was rainy, 0 otherwise), and how many Employees simultaneously worked the shop that day. His data is as follows: Temp Weekend Rainy Employees Sales 80 0 0 3 197 103 0 0 2 200 81 1 1 2 213 73 0 0 4 172 91 0 0 4 177 87 0 0 2 193 77 1 0 3 251 74 0 0 4 182 77 1 1 3 177 He fits the model: Sales = β0 + β1(Temp) + β2(Weekend) + β3(Rainy) + β4(Employees) +εi and estimates the coefficients using linear regression. 1) Find the regression equation. (Round your answers to 4 decimal points) Sales = + (Temp) + (Weekend) + (Rainy)+ (Employees) 2) The owner believes that, everything else held constant, the shop has more sales on weekend days. Test his hypothesis at the α = 0.05 significance level 2.a) Give the null hypothesis for the owner's claim: multiple choice 1 H0: β0 > 0 H0: β0 = 0 H0: β0 < 0 H0: β1 > 0 H0: β1 = 0 H0: β1 < 0 H0: β2 > 0 H0: β2 = 0 H0: β2 < 0 2.b) Give the alternative hypothesis for the owner's claim: multiple choice 2 H1: β0 > 0 H1: β0 = 0 H1: β0 < 0 H1: β1 > 0 H1: β1 = 0 H1: β1 < 0 H1: β2 > 0 H1: β2 = 0 H1: β2 < 0 2.c) Give the t-statistic for this test. (Round your answers to 3 decimal points) 2.d) Give the p-value for this test. (Round your answers to 4 decimal points) 2.e) What do you conclude? multiple choice 3 Reject the null hypothesis. Sales do not increase on weekend days. Do not reject the null hypothesis. Sales do not increase on weekend days. Reject the null hypothesis. Sales increase on weekend days. Do not reject the null hypothesis. Sales t increase on weekend days. 3) Form a 95% confidence interval for the sales increase (in $100's of dollars) on weekends. (Round your answers to 4 decimal points)
Ice Cream
An owner of an ice cream shop wants to determine the factors that affect ice cream sales in a day. Over 9 days, he calculates the Sales (in $100) of the shop, the high temperature that day (Temp), whether it was a Weekend (1 if it was weekend, 0 if it was a weekday), whether it was Rainy that day (1 if it was rainy, 0 otherwise), and how many Employees simultaneously worked the shop that day. His data is as follows:
| Temp | Weekend | Rainy | Employees | Sales |
| 80 | 0 | 0 | 3 | 197 |
| 103 | 0 | 0 | 2 | 200 |
| 81 | 1 | 1 | 2 | 213 |
| 73 | 0 | 0 | 4 | 172 |
| 91 | 0 | 0 | 4 | 177 |
| 87 | 0 | 0 | 2 | 193 |
| 77 | 1 | 0 | 3 | 251 |
| 74 | 0 | 0 | 4 | 182 |
| 77 | 1 | 1 | 3 | 177 |
He fits the model:
Sales = β0 + β1(Temp) + β2(Weekend) + β3(Rainy) + β4(Employees) +εi
and estimates the coefficients using linear regression.
1) Find the regression equation. (Round your answers to 4 decimal points)
Sales = + (Temp) + (Weekend) + (Rainy)+ (Employees)
2) The owner believes that, everything else held constant, the shop has more sales on weekend days. Test his hypothesis at the α = 0.05 significance level
2.a) Give the null hypothesis for the owner's claim:
multiple choice 1
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H0: β0 > 0
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H0: β0 = 0
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H0: β0 < 0
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H0: β1 > 0
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H0: β1 = 0
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H0: β1 < 0
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H0: β2 > 0
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H0: β2 = 0
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H0: β2 < 0
2.b) Give the alternative hypothesis for the owner's claim:
multiple choice 2
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H1: β0 > 0
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H1: β0 = 0
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H1: β0 < 0
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H1: β1 > 0
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H1: β1 = 0
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H1: β1 < 0
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H1: β2 > 0
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H1: β2 = 0
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H1: β2 < 0
2.c) Give the t-statistic for this test. (Round your answers to 3 decimal points)
2.d) Give the p-value for this test. (Round your answers to 4 decimal points)
2.e) What do you conclude?
multiple choice 3
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Reject the null hypothesis. Sales do not increase on weekend days.
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Do not reject the null hypothesis. Sales do not increase on weekend days.
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Reject the null hypothesis. Sales increase on weekend days.
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Do not reject the null hypothesis. Sales t increase on weekend days.
3) Form a 95% confidence interval for the sales increase (in $100's of dollars) on weekends. (Round your answers to 4 decimal points)
Answer: to
4) Give the adjusted R-squared for this regression. (Round your answers to 4 decimal points)
5) Suppose you regress Sales only on Temp, Weekend, and Rainy.
5.a) Give the adjusted R-squared for this regression. (Round your answers to 4 decimal points)
5.b) Which model do you prefer?
multiple choice 4
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The previous model where Sales is regressed on Temp, Weekend, Rainy, and Employees because it has a larger adjusted R-squared value
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This model where Sales is only regressed on Temp, Weekend, and Rainy, because it has a smaller adjusted R-squared value
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There is not enough information to tell.
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