6) 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 ==============================================================================

a. In general, how is a multiple linear regression model used to predict the response variable using predictor variables?

b. What is the equation for your model?

c. What are the results of the overall F-test? Summarize all important steps of this hypothesis test. This includes:

1. Null Hypothesis (statistical notation and its description in words)
2. Alternative Hypothesis (statistical notation and its description in words)
3. Level of Significance
4. Report the test statistic and the P-value in a formatted table as shown below:

Table 3: Hypothesis Test for Overall F-Test

d. Conclusion of the hypothesis test and its interpretation based on the P-value

e. Based on the results of the overall F-test, is at least one of the predictors statistically significant in predicting the number of wins in the season?

f. 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.