Ice Cream Sales Model An owner of an ice cream stand collected 90 days worth of data from last summer. She is attempting to fit a model predicting daily ice cream sales to better operate the stand next summer. She considers the following model: Model 1: Salesi = β0 + β1*Hoursi + β2*HighTempi + β3*(Hoursi*HighTempi) + εi Here, Salesi is the sales in dollars on the ith day, Hoursi is the number of hours the stand was open on the ith day, HighTempi is the high temperature on the ith day, and Hoursi*HighTempi denotes the interaction between hours and high temperature. She fits this model using linear regression. The regression output is as follows: 1) The owner is wanting to test whether there is a significant interaction between number of hours open and the high temperature when predicting sales. 1.a) What is the null hypothesis for her test? multiple choice 1 H0: β1 > 0 H0: β1 < 0 H0: β1 ≠ 0 H0: β1 = 0 H0: β2 > 0 H0: β2 < 0 H0: β2 ≠0 H0: β2 = 0 H0: β3 > 0 H0: β3 < 0 H0: β3 ≠ 0 H0: β3 = 0 1.b) What is the alternative hypothesis for her test? multiple choice 2 HA: β1 > 0 HA: β1 < 0 HA: β1 ≠ 0 HA: β1 = 0 HA: β2 > 0 HA: β2 < 0 HA: β2 ≠0 HA: β2 = 0 HA: β3 > 0 HA: β3 < 0 HA: β3 ≠ 0 HA: β3 = 0 1.c) What is the t-statistic for this test? (Round your answer to 3 decimal points) T-Stat:
Ice Cream Sales Model
An owner of an ice cream stand collected 90 days worth of data from last summer. She is attempting to fit a model predicting daily ice cream sales to better operate the stand next summer. She considers the following model:
Model 1: Salesi = β0 + β1*Hoursi + β2*HighTempi + β3*(Hoursi*HighTempi) + εi
Here, Salesi is the sales in dollars on the ith day, Hoursi is the number of hours the stand was open on the ith day, HighTempi is the high temperature on the ith day, and Hoursi*HighTempi denotes the interaction between hours and high temperature.
She fits this model using linear regression. The regression output is as follows:
1) The owner is wanting to test whether there is a significant interaction between number of hours open and the high temperature when predicting sales.
1.a) What is the null hypothesis for her test?
multiple choice 1
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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: β1 = 0
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H0: β2 > 0
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H0: β2 < 0
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H0: β2 ≠0
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H0: β2 = 0
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H0: β3 > 0
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H0: β3 < 0
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H0: β3 ≠ 0
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H0: β3 = 0
1.b) What is the alternative hypothesis for her test?
multiple choice 2
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HA: β1 > 0
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HA: β1 < 0
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HA: β1 ≠ 0
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HA: β1 = 0
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HA: β2 > 0
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HA: β2 < 0
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HA: β2 ≠0
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HA: β2 = 0
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HA: β3 > 0
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HA: β3 < 0
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HA: β3 ≠ 0
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HA: β3 = 0
1.c) What is the t-statistic for this test? (Round your answer to 3 decimal points)
T-Stat:
1.d) Under the null hypothesis, the t-statistic has a t-distribution with how many degrees of freedom?
Degrees of Freedom:
1.e) Assuming that Model 1 follows the standard regression assumptions, is there significant interaction (at the 5% significance level) between the number of hours open and the high temperature?
multiple choice 3
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Yes, all estimates of regression coefficients are positive.
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Yes, all standard errors are sufficiently small for all regression coefficients.
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Yes, the p-value for the Hours term is less than the significance level.
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Yes, the p-value for the HighTemp term is less than the significance level.
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Yes, the p-value for the Hours:HighTemp term is less than the significance level.
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Yes, the p-value for the F-statistic is less than the significance level.
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No, the p-values for the Hours term and the HighTemp term are both greater than the significance level.
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No, the p-value for the Hours:HighTemp term is greater than the significance level.
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No, the p-value for the F-statistic is less than the significance level.
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There is not enough information to answer this question.
1.f) Suppose, on a given day, the owner is considering staying open for one additional hour. Would the impact on sales be higher if the high temperature that day was 80 degrees or 90 degrees?
multiple choice 4
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80 degrees, since the interaction term is positive and significant.
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80 degrees, since the interaction term is negative and significant.
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90 degrees, since the interaction term is positive and significant.
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90 degrees, since the interaction term is negative and significant.
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It will be the same since the interaction term is not statistically significant.
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There is not enough information to tell.
2) Using this model, predict the sales for the ice cream stand on a day in which it is open for 9 hours and the high temperature is 83. (Round your answer to the nearest dollar)
$
3) The owner considers a second model for predicting ice cream sales:
Model 2: Salesi = β0 + β1*Hoursi + β2*HighTempi + εi
She again fits this model using linear regression. The regression output is as follows:
Which model for predicting sales is preferred?
multiple choice 5
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Model 1, the interaction term is significant.
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Model 1, it has a smaller residual standard error.
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Model 1, it has a larger R-squared value.
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Model 1, it has a larger adjusted R-squared value.
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Model 1, it has a smaller F-statistic.
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Model 2, it has more significant predictors.
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Model 2, it has a larger residual standard error.
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Model 2, it has a smaller R-squared value.
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Model 2, it has a smaller adjusted R-squared value.
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Model 2, it has a larger F-statistic.
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Both models perform the same.
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