Ice Cream Sales ModelAn 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)$= **Linear Regression Results****Call:**The formula used for the linear model is:\[ \text{Income} \sim \text{Hours} + \text{HighTemp} + \text{Hours} \times \text{HighTemp} \]**Residuals:**- Minimum: -68.110- 1st Quartile (1Q): -15.579- Median: 2.773- 3rd Quartile (3Q): 17.245- Maximum: 51.604**Coefficients:**| Predictor | Estimate | Std. Error | t value | Pr(>|t|) ||-----------------|----------|------------|---------|----------|| (Intercept) | 14.5877 | 108.1674 | 0.135 | 0.8930 || Hours | 12.2728 | 14.6225 | 0.839 | 0.4036 || HighTemp | 0.7198 | 1.2264 | 0.587 | 0.5588 || Hours:HighTemp | 0.3364 | 0.1650 | 2.038 | 0.0446 * |**Significance Codes:**- 0 ‘***’- 0.001 ‘**’- 0.01 ‘*’- 0.05 ‘.’- 0.1 ‘ ’- 1**Model Statistics:**- 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**Explanation:**This linear regression model examines the relationship between income and the variables "Hours," "HighTemp," and their interaction. The coefficients table indicates the estimated effects of each predictor. The interaction term "Hours:HighTemp" is statistically significant at the 0.05 level, denoted by '*', suggesting some interaction effect between hours worked and high temperatures on income.The high R-squared value (0.9095) indicates that approximately 91% of the variability in income

The model is given by, Salesi= β0 + β1*Hoursi + β2*HighTempi + β3*(Hoursi*HighTempi) + εi Then the…

Answered: 1m (formula = Income ~ Hours + HighTemp…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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: Sales_i = β₀+ β₁*Hours_i + β₂*HighTemp_i+ β₃*(Hours_i*HighTemp_i)+ ε_i

Here, Sales_iis the sales in dollars on the ith day, Hours_iis the number of hours the stand was open on the ith day, HighTemp_iis the high temperature on the ith day, and Hours_i*HighTemp_idenotes 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)