7)Multiple Regression: Predicting the Total Number of Wins using Average Points Scored, Average Relative Skill, Average Points Differential, and Average Relative Skill Differential

Given the data, answer the questions below:

OLS Regression Results ============================================================================== Dep. Variable: total_wins R-squared: 0.878

Model: OLS Adj. R-squared: 0.877

Method: Least Squares F-statistic: 1102.

Date: Tue, 14 Feb 2023 Prob (F-statistic): 3.07e-278

Time: 04:18:20 Log-Likelihood: -1815.5

No. Observations: 618 AIC: 3641.

Df Residuals: 613 BIC: 3663.

Df Model: 4

Covariance Type: nonrobust ========================================================================================

coef std err t P>|t| [0.025 0.975]

----------------------------------------------------------------------------------------

Intercept 34.5753 25.867 1.337 0.182 -16.223 85.373

avg_elo_n -0.0134 0.017 -0.769 0.442 -0.048 0.021

avg_pts 0.2597 0.043 6.070 0.000 0.176 0.344

avg_pts_differential 1.6206 0.135 12.024 0.000 1.356 1.885

avg_elo_differential 0.0525 0.018 2.915 0.004 0.017 0.088

============================================================================== Omnibus: 193.608 Durbin-Watson: 0.979

Prob(Omnibus): 0.000 Jarque-Bera (JB): 598.416

Skew: -1.503 Prob(JB): 1.14e-130

Kurtosis: 6.769 Cond. No. 2.11e+05 ====================================================

• What are the results of individual t-tests for the parameters of each predictor variable? Is each of the predictor variables statistically significant based on its P-value? Use a 1% level of significance.
• Report and interpret the coefficient of determination.
• What is the predicted total number of wins in a regular season for a team that is averaging 75 points per game with a relative skill level of 1350, average point differential of -5 and average relative skill differential of -30?
• What is the predicted total number of wins in a regular season for a team that is averaging 100 points per game with a relative skill level of 1600, average point differential of +5 and average relative skill differential of +95?