4. Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill You created a simple linear regression model for the total number of wins in a regular season using the average relative skill as the predictor variable. See Step 3 in the Python script to address the following items: In general, how is a simple linear regression model used to predict the response variable using the predictor variable? 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 1: 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. e. Conclusion of the hypothesis test and its interpretation based on the P-value . Based on the results of the overall F-test, can average relative skill predict the total number of wins in the regular season? . What is the predicted total number of wins in a regular season for a team that has an average relative skill of 1550? Round your answer down to the nearest integer. What is the predicted number of wins in a regular season for a team that has an average relative skill of 1450? Round your answer down to the nearest integer.7. Multiple Regression: Predicting the Total Number of Wins using Average Points Scored, Average Relative Skill, Average Points Differential, and Average Relative Skill Differential You created a multiple regression model with the total number of wins as the response variable, with average points scored, average relative skill, average points differential, and average relative skill 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) 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 +5 and average relative skill differential of +95?8. Conclusion Describe the results of the statistical analyses clearly, using proper descriptions of statistical terms and concepts. Fully describe what these results mean for your scenario. Briefly summarize your findings in plain language. What is the practical importance of the analyses that were performed?Step 1: Data Preparation calculate the number of wins for teams in a basketbat regular season between the years 1995 and 2015. Click the block of code below and hit the Run button above. import pandas as po from Ipython alsplay import display , WTF how wins of - pd road cav( ' now _ wins _ data . cav " ) display(HTML (rba_wins_of, heas();to_html()) print( husker of rows in the dataset -". len(nba_wins_SF)) BuckS 10 -OPP_Pts ava_clo_ ava_ opp_elo_nava_pts_differential avg_clo_ differential local_ wins 1 195 Bulls 101.524390 36 695122 1569 892129 1488 199352 4623268 1542 438391 1496 848261 0.621951 43 585130 9 195 Celis 102 760486 104 650537 1431.307532 1495 506224 1.878049 95 Cippers 96.670732 105 629260 1309 063701 1517 260260 9.158537 -208 206568 cumber of rows in the dataset - 6is Step 2: Scatterplot and Correlation for the Total Number of Wins and Average Relative Your coach expects teams to win more games in a regular season if the cted that the total number of wins and the average relative kil are correlated. Calculate the Pearson correlation coencient and its P-value. Make the following eats to me code block below. 1. Replace 79DATAFRAME_NAME?? with the name of the da place 79RELATIVE_SKILL ?2 WIN In red in this project See Step to pick the variable name. Enclose this variable in single quotes. For example. If the variable name is vart then replace ?7RELATIVE_ SKILL?? with see the table included in the Project These instructions above to pick the variable name. Enclose this variable in single quotes For example, " the code stock below wil print a scatterplot of the total number of wins against the average relative skin. After you are done with your edits, click the block of code below and but the Run button above In (7]: inport scapy.stats as st pit . plot (rba_wins_ of[ ave pts ], nba_wins_of ["total_wins'], '6") pit. title(" Total humber of wins by Average Relative Skill', fontsize-20) pit. ylabel( Total Number of wins , correlation coefficient, p_value - st. pearsonr(nba_wins_ of['ava_pts'1. nba_wins_of["total_wins"]) Primed -pearson correlation coefficient"-," round(correlation coefficient,4)) Total Number of Wins by Average Relative Skill earsbotcon betwen p.vaiup correlation Coefficient . Skill and the Total Number of Wins Step 3: Simple Linear Regression: Predicting the Total Number of Wins using Average Relative The coach of your team suggests a simple linear regression model with the total number of wins as the response variable and the average relive skill as the coach predict how many games your team might win in a regular season. Create this simple Inca code block below. to pick the variable name . Do not enclose mis variable in quotes. For example, if the variable name is wart then replace 77RESPONSE _VARIABLE7? wth vart. the variable name . Do not enclose this variable in quotes. For example. If the variable name is vara then replace ?7PREDICTOR VARIABLE?? with above to pick be modepress the variable names are vari for the rest (8]: inport statsmodels. formula. apt as saf . Staple Linear Regression Print ( models . summary() ) OLS Regression Results Dep. variable : Model: OLs As] . R-squared : Time: Sun, 11 Dec 2022 Prob (f-statistic) : No. Observations: 21 Log-Likel of model : coverlance Type: coof std eer t Pit| [0.625 0.975] Intercept Bgets 1:2849 -193.820 -67.275 Frob(Omnibus) : kurtosis: 42.Cond. No. 1] Standard Errors assume that the covariance matrix of, the errors is correctly specified. strong multicollinearity or other muserical problems. Step 4: Scatterplot and Correlation for the Total Number of Wins and Average Points ing are higher * a team maintains high average points scored. Therefore. It is expected that the total number of wins and th coencient and its P-value. Make the following eats to the code block belts and the average points scored are AFRAME NAME ?? with the name of the dataframe uses in this project. See Step 1 for the name of dataframe used in this project Replace ?7POINTSTo win the name some venable re everton shirts areredle , Partly season fee the bible included in the Project Three POINTS?? with vart. See the table included in the Project Three instructions above to pick the variable name. Enclose this variable in single quotes. For example, # the vanable name is varz then replace ?7wrSummons above to pi of wins against the average ed in a regular season. After you are done with your edits. cack the block of code below and hit the Run bution above. n [9]: inport scapy.stats as st pit . plot ( be wins_off ave clo.n'], res_wins_ off" total_wins"], "o") pit. title(" Total humber of Mins by Average points Scored'. fontsize-26) pit. ylabel( Total Number of wins" correlation coefficient , p_value - st. pear prime("Correlation between Average Points Scored ir (goa_wins_off'avg.elo_n"], rba_wins_off"total_wins"1) prince"p-value - , rounder shift sjoint - . ro could(correlation coefficient,4)) Total Number of Wins by Average Points Scored searsin correlation courage Points scored and the Step 5: Multiple Regression: Predicting the Total Number of Wins using Average Points Scored and Average Relative Skill variable are the newsmen's george and she moredes the coach you can suggest a multiple regression model with the total number of wins as the response cansore and the average points scored and the average relative skill as predictor vanso because you expect more he following eats to the code brock performance metric to determine the total number of wins in a regular season Cre on model Math Replace ?7RESPONSE VARIABLE ?? wih the variable name that is being predicted, See the bible included in the Project Three Instruction Instructions above . Do not enclose thes variable in quotes. For example, " the variable name is vart then replace 77PREDICTOR VARIABLE_177 with Structions anEDITOR VARIABLE the Yaable seven PREDICTOR VARIABLE 277 with should be: model = smit. cis(vard - var + vary. nba_wins_on.al() After you are done with your edes, cack the block of code below and but the Run bution above in [16]: import statsmodels. formula. apt as saf "odelz - sof . ols( total ving " avg ets + avg_elo_n' , who_wins_of).fit( ) .OLS Regression Result. Dep. Variable: total-wing boy! A-squared: method: Cover lance Type: ave pts Frob(omnibus): Soe Jarque-Bers (jg); 1 Standard Errors assume that the covariance matrix of the arrees is correctly specified. strong multicollinearity or other suserical' this right and Step 6: Multiple Regression: Predicting the Total Number of Wins using Average Points Differential The coach also wants you to consider the average points differential and average relative stil differential as predictor variables in the triple regression ofcl. Create a mutiple regression model with the total number of wins as the response variable, and average points scored, average relative skill, average between the team and felon based on metrics like the average score. average relative skos, average points differential and average relative skal differentsal You are to write this code block yourself. Use Step S to help you write this code block Here is some Inform mon that will help you The cataframe used in this project is called nog_wins_cf. e variable "avg_clo_now represents average relative skil of each team in a regular season arable "avg_elo_differenz our code in the cose block section below After you are done. cack this block of cose and hit the Ru need more help with this step. ach out to your instructor if you n Ized inport statsmodels. formula, api as she modelz - seif . ols( total wine - avg pts + avg_ele_n + avg_pts_differential" . print ( modelz summary() ) OLS Regression Results Dep. Variable: Model: total-vous Adj. A-squared: sun, at Squares Fustatistiet of Model: Cover Lance Type: coef std err Intercept avg_pts_differential Cenibus: Prob(omnibus ) : standard Errors assume that the coreraines ferraz er Thy Breech t's correctly specified. ther nuserical