Question

1. Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor variables. See Step 5 in the Python script. How might the car rental company use this model?

2.                             OLS Regression Results                            
   ==============================================================================
   Dep. Variable:                    mpg   R-squared:                       0.858
   Model:                            OLS   Adj. R-squared:                  0.848
   Method:                 Least Squares   F-statistic:                     81.68
   Date:                Thu, 11 Jun 2020   Prob (F-statistic):           3.54e-12
   Time:                        10:50:26   Log-Likelihood:                -67.238
   No. Observations:                  30   AIC:                             140.5
   Df Residuals:                      27   BIC:                             144.7
   Df Model:                           2                                         
   Covariance Type:            nonrobust                                         
   ==============================================================================
                    coef    std err          t      P>|t|      [0.025      0.975]
   ------------------------------------------------------------------------------
   Intercept     38.6824      1.580     24.490      0.000      35.442      41.923
   wt            -4.4178      0.623     -7.094      0.000      -5.696      -3.140
   hp            -0.0310      0.008     -3.689      0.001      -0.048      -0.014
   ==============================================================================
   Omnibus:                        2.445   Durbin-Watson:                   1.990
   Prob(Omnibus):                  0.295   Jarque-Bera (JB):                1.732
   Skew:                           0.589   Prob(JB):                        0.421
   Kurtosis:                       2.998   Cond. No.                         604.
   ==============================================================================
   
   Warnings:
   [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Answer 1

Question 1:

Write the multiple regression equation for miles per gallon as the response variable. Use weight and horsepower as predictor variables.

The Multiple Regression Equation is:

y = 38.6824 - 4.4178 wt - 0.031 hp,

where

y = Miles per gallon (Response Variable)

wt = Weight (Predictor Variable 1)

hp = Horsepower (Predictor Variable 2)

Question 2:

How might the car rental company use this model?

The car rental company might use this model by noting the following informations derived from Multiple Regression Equation:

(i)

For every increase of 1 unit of weight, the Miles per gallon decreases by 4.4178 units

(ii)

For every increase of 1 unit of Horsepowert, the Miles per gallon decreases by 0.031 units