Do heavier cars use more gasoline? To answer this question, a researcher randomly selected 15 cars. He collected their weight (in hundreds of pounds) and the mileage (MPG) for each car. From a scatterplot made with the data, a linear model seemed appropriate which is included as a photo. What proportion of the variation in mileage is accounted for by the linear relationship with the wight of the car? And if we wanted to test if there is a significant straight-line relationship between the weight and the mileage of a car, we can perform a T test. Give the value of the t statistic for this test. ### Linear Regression AnalysisThe table presents the results of a linear regression analysis. Below is a detailed explanation of the provided statistical output:#### Model Summary- **R-Square:** 0.438 - This value indicates that approximately 43.8% of the variability in the dependent variable can be explained by the model. - **Root MSE (Mean Squared Error):** 6.78 - This is a measure of the standard deviation of the residuals. It provides an estimate of how much the actual data points deviate from the predicted values.#### CoefficientsThe table includes various statistics for each parameter in the model:1. **Intercept** - **Estimate:** 40.439 - This is the predicted value when all other variables are zero. - **Standard Error:** 6.275 - This measures the accuracy of the coefficient estimate. - **t Value:** 6.445 - This statistic is used to test the hypothesis that the coefficient is different from zero. - **Pr > |t|:** 0.0000 - The p-value indicates the probability that the coefficient is actually zero. A very small p-value suggests statistical significance.2. **WEIGHT** - **Estimate:** -0.521 - This coefficient represents the change in the dependent variable for a one-unit increase in WEIGHT, holding other variables constant. - **Standard Error:** 0.164 - This indicates the variability in the estimate. - **t Value:** -3.182 - Suggests the strength of evidence against a null hypothesis of no effect. - **Pr > |t|:** 0.0072 - A p-value less than 0.05 typically indicates that the effect is statistically significant.This output provides insights into the relationship between the independent variable, WEIGHT, and the dependent variable in the model, along with the reliability and significance of these estimates.

Given info: A researcher randomly selected 15 cars. He collected their weight (in hundreds of pounds) and the mileage (MPG) for each car. Here, the dependent variable is mileage and the independent variable is weight.From the given output, the value of R2 is 0.438. The value of coefficient of determination tells the proportion of variance in dependent variable that is explained by the independent variable(s). The proportion of the variation in mileage is accounted for by the linear relationship with the wight of the car is 0.438. And if we wanted to test if there is a significant straight-line relationship between the weight and the mileage of a car, we can perform a T test. From the given output, the value of the t statistic for this test is observed to be -3.182.