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:

a$.$ Null Hypothesis $($statistical notation and its description in words$)$

b$.$ Alternative Hypothesis $($statistical notation and its description in words$)$

c$.$ Level of Significance

d$.$ 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.

e$.$ 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 OLS Regression Results

$==============================================================================$

Dep. Variable: total$\_$wins R$-$squared: $0\mathrm{.}878$

Model: OLS Adj. R$-$squared: $0\mathrm{.}877$

Method: Least Squares F$-$statistic: $1102.$

Date: Sun, $25$ Feb $2024$ Prob $($F$-$statistic$)$: $3\mathrm{.}07$e$-278$

Time: $21$:$36$:$25$ Log$-$Likelihood: $-1815\mathrm{.}5$

No$.$ Observations: $618$ AIC: $3641.$

Df Residuals: $613$ BIC: $3663.$

Df Model: $4$

Covariance Type: nonrobust

$========================================================================================$

coef std err t P$>|$t$|[0\mathrm{.}0250\mathrm{.}975]$

$----------------------------------------------------------------------------------------$

const $34\mathrm{.}575325\mathrm{.}8671\mathrm{.}3370\mathrm{.}182-16\mathrm{.}22385\mathrm{.}373$

avg$\_$pts $0\mathrm{.}25970\mathrm{.}0436\mathrm{.}0700\mathrm{.}0000\mathrm{.}1760\mathrm{.}344$

avg$\_$elo$\_$n $-0\mathrm{.}01340\mathrm{.}017-0\mathrm{.}7690\mathrm{.}442-0\mathrm{.}0480\mathrm{.}021$

avg$\_$pts$\_$differential $1\mathrm{.}62060\mathrm{.}13512\mathrm{.}0240\mathrm{.}0001\mathrm{.}3561\mathrm{.}885$

avg$\_$elo$\_$differential $0\mathrm{.}05250\mathrm{.}0182\mathrm{.}9150\mathrm{.}0040\mathrm{.}0170\mathrm{.}088$

$==============================================================================$

Omnibus: $193\mathrm{.}608$ Durbin$-$Watson: $0\mathrm{.}979$

Prob$($Omnibus$)$: $0\mathrm{.}000$ Jarque$-$Bera $($JB$)$: $598\mathrm{.}416$

Skew: $-1\mathrm{.}503$ Prob$($JB$)$: $1\mathrm{.}14$e$-130$

Kurtosis: $6\mathrm{.}769$ Cond. No$.2\mathrm{.}11$e$+05$

$==============================================================================$

Warnings:

$[1]$ Standard Errors assume that the covariance matrix of the errors is correctly specified.

$[2]$ The condition number is large, $2\mathrm{.}11$e$+05.$ This might indicate that there are

strong multicollinearity or other numerical problems.$+5$ and average relative skill differential of $+95?$