You created a multiple regression model with the total number of wins as the response variable, with average points scored, average relative skill, and average points differential as predictor variables.
See Step 6 in the Python script to answer the following questions:
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:
Null Hypothesis (statistical notation and its description in words)
Alternative Hypothesis (statistical notation and its description in words)
Level of Significance
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.
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 and average point differential of -5?
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 and average point differential of +5?
OLS Regression Results
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Dep. Variable: total_wins R-squared: 0.876
Model: OLS Adj. R-squared: 0.876
Method: Least Squares F-statistic: 1449.
Date: Thu, 15 Oct 2020 Prob (F-statistic): 5.03e-278
Time: 00:22:22 Log-Likelihood: -1819.8
No. Observations: 618 AIC: 3648.
Df Residuals: 614 BIC: 3665.
Df Model: 3
Covariance Type: nonrobust
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coef std err t P>|t| [0.025 0.975]
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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 <---this is relative skill
avg_pts_differential 1.7621 0.127 13.928 0.000 1.514 2.011
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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