• 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 2: Hypothesis Test for the 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 total 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?
• What is the predicted total number of wins in a regular season for a team that is averaging 100 points per game with an average relative skill level of 1600?

This is the data:

OLS Regression Results ============================================================================== Dep. Variable: total_wins R-squared: 0.837 Model: OLS Adj. R-squared: 0.837 Method: Least Squares F-statistic: 1580. Date: Sun, 17 Apr 2022 Prob (F-statistic): 4.41e-243 Time: 23:54:48 Log-Likelihood: -1904.6 No. Observations: 618 AIC: 3815. Df Residuals: 615 BIC: 3829. Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ Intercept -152.5736 4.500 -33.903 0.000 -161.411 -143.736 avg_pts 0.3497 0.048 7.297 0.000 0.256 0.444 avg_elo_n 0.1055 0.002 47.952 0.000 0.101 0.110 ============================================================================== Omnibus: 89.087 Durbin-Watson: 1.203 Prob(Omnibus): 0.000 Jarque-Bera (JB): 160.540 Skew: -0.869 Prob(JB): 1.38e-35 Kurtosis: 4.793 Cond. No. 3.19e+04 ============================================================================== Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. [2] The condition number is large, 3.19e+04. This might indicate that there are strong multicollinearity or other numerical problems.