1. You created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. Does the graph show any trend? If yes, is the trend what you expected? Why or why not? See Step 2
2. What is the coefficient of correlation between miles per gallon and weight? What is the sign of the correlation coefficient? Does the coefficient of correlation indicate a strong correlation, weak correlation, or no correlation between the two variables? How do you know? See Step 3
3. Write the simple linear regression equation for miles per gallon as the response variable and weight as the predictor variable. How might the car rental company use this model? See Step 4.
4. What is the slope coefficient? Is this coefficient significant at a 5% level of significance (alpha=0.05)? (Hint: Check the P-value, , for weight ) See Step 4

Step 1

Step 2

Step 3

Step 4

Step 5

Unnamed: 0 mpg cyl disp hp drat wt qsec VS am gear carb 11 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 1 6 160.0 110 3.90 2.875 17.02 0 11 4 4 31 Mazda RX4 Wag 21.0 Volvo 142E 21.4 Merc 450SLC 15.2 4 121.0 109 4.11 2.780 18.60 1 1 4 2 13 8 275.8 180 3.07 3.780 18.00 3 3 6 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 3 4 MPG against Weight 35 3 30 25 MPG 20 15 10 1.5 2.0 2.5 4.5 5.0 5.5 3.0 3.5 4.0 Weight (1000s lbs) MPG against Horsepower 35 30 25 MPG 20 . 15 10 50 100 150 250 300 200 Horsepower mpg wt hp mpg 1.000000 -0.871514 -0.776374 wt -0.871514 1.000000 0.670329 hp -0.776374 0.670329 1.000000 OLS Regression Results ====EE Dep. Variable: Model: Method: Date: Time: No. Observations: Df Residuals: Df Model: Covariance Type: mpg OLS Least Squares Wed, 10 Jun 2020 16:38:41 30 R-squared: Adj. R-squared: F-statistic: Prob (F-statistic): Log-Likelihood: AIC: BIC: 0.827 0.814 64.36 5.33e-11 - 70.109 146.2 150.4 27 2 nonrobust coef std err t P>|t| [0.025 0.975] Intercept wt 37.2342 -3.8673 -0.0313 1.628 0.655 0.010 22.877 -5.904 -3.232 0.000 0.000 0.003 33.895 -5.211 -0.051 40.574 -2.523 -0.011 hp Omnibus: Prob (Omnibus): Skew: Kurtosis: 4.184 0.123 0.774 3.207 Durbin-Watson: Jarque-Bera (JB): Prob(JB): Cond. No. 1.968 3.045 0.218 561. Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. Unnamed: 0 mpg cyl disp hp drat wt qsec VS am gear carb 11 Merc 450SE 16.4 8 275.8 180 3.07 4.070 17.40 0 0 3 1 6 160.0 110 3.90 2.875 17.02 0 11 4 4 31 Mazda RX4 Wag 21.0 Volvo 142E 21.4 Merc 450SLC 15.2 4 121.0 109 4.11 2.780 18.60 1 1 4 2 13 8 275.8 180 3.07 3.780 18.00 3 3 6 Duster 360 14.3 8 360.0 245 3.21 3.570 15.84 0 3 4 MPG against Weight 35 3 30 25 MPG 20 15 10 1.5 2.0 2.5 4.5 5.0 5.5 3.0 3.5 4.0 Weight (1000s lbs) MPG against Horsepower 35 30 25 MPG 20 . 15 10 50 100 150 250 300 200 Horsepower mpg wt hp mpg 1.000000 -0.871514 -0.776374 wt -0.871514 1.000000 0.670329 hp -0.776374 0.670329 1.000000 OLS Regression Results ====EE Dep. Variable: Model: Method: Date: Time: No. Observations: Df Residuals: Df Model: Covariance Type: mpg OLS Least Squares Wed, 10 Jun 2020 16:38:41 30 R-squared: Adj. R-squared: F-statistic: Prob (F-statistic): Log-Likelihood: AIC: BIC: 0.827 0.814 64.36 5.33e-11 - 70.109 146.2 150.4 27 2 nonrobust coef std err t P>|t| [0.025 0.975] Intercept wt 37.2342 -3.8673 -0.0313 1.628 0.655 0.010 22.877 -5.904 -3.232 0.000 0.000 0.003 33.895 -5.211 -0.051 40.574 -2.523 -0.011 hp Omnibus: Prob (Omnibus): Skew: Kurtosis: 4.184 0.123 0.774 3.207 Durbin-Watson: Jarque-Bera (JB): Prob(JB): Cond. No. 1.968 3.045 0.218 561. Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified