1m (formula = Income ~ Hours + HighTemp + Hours * HighTemp) Residuals: Min 1Q Median 3Q Max -68.110 -15.579 2.773 17.245 51.604 Coefficients: (Intercept) Hours High Temp 0.7198 Hours:High Temp 0.3364 --- Estimate Std. Error t value Pr(>|t|) 14.5877 108.1674 0.135 12.2728 14.6225 0.839 1.2264 0.587 0.1650 2.038 0.8930 0.4036 0.5588 0.0446 * Signif. codes: 0 ****' 0.001 '**' 0.01 * 0.05 '.' 0.1'' 1 Residual standard error: 25.09 on 86 degrees of freedom Multiple R-squared: 0.9095, Adjusted R-squared: 0.9063 F-statistic: 288 on 3 and 86 DF, p-value: < 2.2e-16
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.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:
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)
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