• In general, how is a multiple linear regression model used to predict the response variable using predictor variables?
• What is the equation for your model?
• 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

Statistic	Value
Test Statistic	X.XX *Round off to 2 decimal places.
P-value	X.XXXX *Round off to 4 decimal places.

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

• 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?
• 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?

This is my data:

OLS Regression Results ============================================================================== Dep. Variable: total_wins R-squared: 0.876 Model: OLS Adj. R-squared: 0.876 Method: Least Squares F-statistic: 1449. Date: Sun, 17 Apr 2022 Prob (F-statistic): 5.03e-278 Time: 23:56:49 Log-Likelihood: -1819.8 No. Observations: 618 AIC: 3648. Df Residuals: 614 BIC: 3665. Df Model: 3 Covariance Type: nonrobust ======================================================================================== coef std err t P>|t| [0.025 0.975] ---------------------------------------------------------------------------------------- Intercept -35.8921 9.252 -3.879 0.000 -54.062 -17.723 avg_pts 0.2406 0.043 5.657 0.000 0.157 0.324 avg_elo_n 0.0348 0.005 6.421 0.000 0.024 0.045 avg_pts_differential 1.7621 0.127 13.928 0.000 1.514 2.011 ============================================================================== Omnibus: 181.805 Durbin-Watson: 0.975 Prob(Omnibus): 0.000 Jarque-Bera (JB): 506.551 Skew: -1.452 Prob(JB): 1.01e-110 Kurtosis: 6.352 Cond. No. 7.51e+04 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. [2] The condition number is large, 7.51e+04. This might indicate that there are strong multicollinearity or other numerical problems.