In: Step 6: Multiple Regression: Predicting the Total Number of Wins using Average Points Scored, Average Relative Skill, Average Points Differential and Average Relative Skill Differential The coach also wants you to consider the average points differential and average relative skill differential as predictor variables in The multiple regression model. Create a multiple regression model with the total number of wins as the response variable. and average points scored, average relative skill, average points differential and average relative skill differential as predictor variables. This regression model will help your coach predict how many games your team might win in a regular season based on metrics like the average score. average relative skill, average points ditferential and average relative skill differential between the team and their opponents. You are to write this code block yourself. Use Step 5 to help you write this code block. Here is some intomration that will help you write this code block. Reach out to your instructor it you need help. 1. The dataframe used in this project is called nba_wins_dt. 2. The variable avg Jits represents average points scored by each team in a regular season. 3. The variable avg_elo_n represents average relative skill of each team in a regular season. 4. The variable avg Jits_dii'lerential represents average points differential between each team and Their opponents in a regular season. 5. The variable avg_elo_ditferential represents average relative skill differential between each team and their opponents in a regular season. 6. Print the model summary. 1r.I'|r|'rite your code in the code block section below. After you are done, click this block of code and hit the Run button above. Reach out to your instructor it you need more help with This step. # Write your code in this code block section Project Three: Simple Linear Regression and Multiple Regression This notebook contains step-by-step directions for Project Three. It is very important to run through the steps in order. Some steps depend on the outputs of earlier steps. Once you have completed the steps in this notebook, be sure to write your summary report. You are a data analyst for a basketball team and have access to a large set of historical data that you can use to analyze performance patterns. The coach of the team and your management have requested that you come up with regression models that predict the total number of wins for a team in the regular season based on key performance metrics. Although the data set is the same that you used in the previous projects, the data set used here has been aggregated to study the total number of wins in a regular season based on performance metrics shown in the table below. These regression models will help make key decisions to improve the performance of the team. You will use the Python programming language to perform the statistical analyses and then prepare a report of your findings to present for the team's management. Since the managers are not data analysts, you will need to interpret your findings and describe their practical implications. There are four important variables in the data set that you will utilize in Project Three. Variable What does it represent total_wins Total number of wins in a regular season avg_pts Average points scored in a regular season avg_elo_n Average relative skill of each team in a regular season avg_pts_differential Average point differential between the team and their opponents in a regular season avg_elo_differential Average relative skill differential between the team and their opponent in a regular season The average relative skill (represented by the variable avg_elo_n in the data set) is simply the average of a team's relative skill in a regular season. Relative skill is measured using the ELO rating. This measure is inferred based on the final score of a game, the game location, and the outcome of the game relative to the probability of that outcome. The higher the number, the higher the relative skill of a team. Reminder: It may be beneficial to review the summary report document for Project Three prior to starting this Python script. That will give you an idea of the questions you will need to answer with the outputs of this script.Step 1: Data Preparation This step uploads the data set from a CSV file and transforms the data into a form that will be used to create regression models. The data will be aggregated to calculate the number of wins for teams in a basketball regular season between the years 1995 and 2015. Click the block of code below and hit the Run button above. In [1]: import numpy as np import pandas as pd import scipy . stats as st import matplotlib. pyplot as plt from IPython. display import display, HTML # dataframe for this project nba_wins_df = pd. read_csv('nba_wins_data. cev' ) display (HTML(nba_wins_df . head() . to_html() ) ) print("printed only the first five observations...") print("Number of rows in the dataset =", len(nba_wins_df) ) year_id fran_id avg_pts avg_opp_pts avg_elo_n avg_opp_elo_n avg_pts_differential avg_elo_differential total_wins 1995 Bucks 99.341463 103.707317 1368.604789 1497.311587 -4.365854 128.706798 34 1 1995 Bulls 101.524390 96 695122 1569.892129 1488. 199352 4.829268 81.692777 47 2 1995 Cavaliers 90.451220 89.829268 1542.433391 1498.848261 0.621951 43.585130 43 3 1995 Celtics 102.780488 104.658537 1431.307532 1495.936224 -1.878049 -64.628693 35 4 1995 Clippers 96.670732 105.829268 1309.053701 1517.260260 -9.158537 -208.206558 17 printed only the first five observations... Number of rows in the dataset = 618Step 2: Scatterplot and Correlation for the Total Number of Wins and Average Relative Skill Your coach expects teams to win more games in a regular season if they have a higher average relative skill compared to their opponents. This is because the chances of winning are higher if a team can maintain high average relative skill. Therefore, it is expected that the total number of wins and the average relative skill are correlated. Calculate the Pearson correlation coefficient and its P-value. Make the following edits to the code block below: 1. Replace ??DATAFRAME_NAME?? with the name of the dataframe used in this project. See Step 1 for the name of dataframe used in this project. 2. Replace ??RELATIVE_SKILL?? with the name of the variable for average relative skill. See the table included in the Project Three instructions above to pick the variable name. Enclose this variable in single quotes. For example, if the variable name is var1 then replace ??RELATIVE_SKILL?? with 'var1' 3. Replace ??WINS?? with the name of the variable for the total number of wins in a regular season. Remember to enclose the variable in single quotes. See the table included in the Project Three instructions above to pick the variable name. Enclose this variable in single quotes. For example, if the variable name is var2 then replace ??WINS?? with "var2". The code block below will print a scatterplot of the total number of wins against the average relative skill. After you are done with your edits, click the block of code below and hit the Run button above. In [7]: import scipy. stats as st --- TODO: make your edits here --- plt. plot(nba_wins_df['avg_elo_n' ], nba_wins_df[ 'total_wins' ], 'o') plt. title( 'Total Number of Wins by Average Relative Skill' , fontsize=20) pit. xlabel( 'Average Relative Skill' ) plt. ylabel( 'Total Number of Wins' ) plt. show() # - --- TODO: make your edits here - --- correlation_coefficient, p_value = st. pearsonr(nba_wins_df['avg_elo_n' ], nba_wins_df[ 'total_wins' ]) print("Correlation between Average Relative Skill and the Total Number of Wins ") print( "Pearson Correlation Coefficient =", round(correlation_coefficient,4) ) print("P-value =", round(p_value,4) ) Total Number of Wins by Average Relative Skill 70 60 50 Total Number of Wins 40 30 20 10 1200 1300 1400 1500 1600 1700 1800 Average Relative Skill Correlation between Average Relative Skill and the Total Number of Wins Pearson Correlation Coefficient = 0.9072 P-value = 0.0Step 3: Simple Linear Regression: Predicting the Total Number of Wins using Average Relative Skill The coach of your team suggests a simple linear regression model with the total number of wins as the response variable and the average relative skill as the predictor variable. He expects a team to have more wins in a season if it maintains a high average relative skill during that season. This regression model will help your coach predict how many games your team might win in a regular season. Create this simple linear regression model. Make the following edits to the code block below: 1. Replace ??RESPONSE_VARIABLE?? with the variable name that is being predicted. See the table included in the Project Three instructions above to pick the variable name. Do not enclose this variable in quotes. For example, if the variable name is var1 then replace ??RESPONSE_VARIABLE?? with var1. 2. Replace ??PREDICTOR_VARIABLE?? with the variable name that is the predictor. See the table included in Project Three instructions above to pick the variable name. Do not enclose this variable in quotes. For example, if the variable name is var2 then replace ??PREDICTOR_VARIABLE?? with var2. For example, if the variable names are var1 for the response variable and var2 for the predictor variable, then the expression in the code block below should be: model = smf.ols(var1 - var2', nba_wins_df).fit() After you are done with your edits, click the block of code below and hit the Run button above. In [8]: import statsmodels. formula. api as smf # Simple Linear Regression # - --- TODO: make your edits here --- modell = smf . ols( 'total_wins ~ avg_elo_n', nba_wins_df) . fit() print (modell . summary ( ) ) OLS Regression Results Dep. Variable: total_wins R-squared; 0. 823 Model OLS Adj. R-squared: . 823 Method : Least Squares F-statistic: 2865. Date: Sat, 18 Jun 2022 Prob (F-statistic) : 8. 06e-234 Time : 22:36:41 Log-Likelihood 1930.3 No. Observations : 618 AIC: 3865. of Residuals: 616 BIC 3873. of Model: 1 Covariance Type: nonrobust zoet std err P> | t 0.025 0.975] Intercept -128. 2475 3.149 -40. 731 0.006 134.431 -122.064 avg_elo_r 0. 1121 0.602 53.523 0.060 0.108 0. 116 Omnibus : 152.822 Durbin-Watson: 1. 098 Prob (Omnibus ) : 0.060 Jarque-Bera (JB): 393. 223 Skew: -1.247 Prob (JB) : 4. 10e-86 Kurtosis : 6.009 Cond. No. 2.14e+04 Warnings : [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. [2] The condition number is large, 2.14e+04. This might indicate that there are strong multicollinearity or other numerical problems.Step 4: Scatterplot and Correlation for the Total Number of Wins and Average Points Scored Your coach expects teams to win more games in a regular season if they score more points on average during the season. This is because the chances of winning are higher if a team maintains high average points scored. Therefore, it is expected that the total number of wins and the average points scored are correlated. Calculate the Pearson correlation coefficient and its P-value. Make the following edits to the code block below: 1. Replace ??DATAFRAME_NAME?? with the name of the dataframe used in this project. See Step 1 for the name of dataframe used in this project. 2. Replace ??POINTS?? with the name of the variable for average points scored in a regular season. See the table included in the Project Three instructions above to pick the variable name. Enclose this variable in single quotes. For example, if the variable name is var1 then replace ??POINTS?? with "var1'. 3. Replace ??WINS?? with the name of the variable for the total number of wins in a regular season. Remember to enclose the variable in single quotes. See the table included in the Project Three instructions above to pick the variable name. Enclose this variable in single quotes. For example, if the variable name is var2 then replace ??WINS?? with "var2" The code block below will print a scatterplot of the total number of wins against the average points scored in a regular season. After you are done with your edits, click the block of code below and hit the Run button above. In [9]: import scipy. stats as st -- TODO: make your edits here -- plt. plot(nba_wins_df['avg_pts' ], nba_wins_df[ 'total_wins' ], 'o') plt. title( 'Total Number of Wins by Average Points Scored', fontsize=20) pit . xlabel('Average Points Scored' ) plt. ylabel( 'Total Number of Wins' ) pit . show( ) ---- TODO: make your edits here - --- correlation_coefficient, p_value = st. pearson(nba_wins_df['avg_pts' ], nba_wins_df[ 'total_wins' ]) print("Correlation between Average Points Scored and the Total Number of Wins ") print("Pearson Correlation Coefficient =", round(correlation_coefficient,4) ) print("P-value =", round(p_value,4) ) Total Number of Wins by Average Points Scored 70 60 : 50 Total Number of Wins 40 30 20 95 100 105 110 Average Points Scored Correlation between Average Points Scored and the Total Number of Wins Pearson Correlation Coefficient = 0.4777 P-value = 0.0Step 5: Multiple Regression: Predicting the Total Number of Wins using Average Points Scored and Average Relative Skill Instead of presenting a simple linear regression model to the coach, you can suggest a multiple regression model with the total number of wins as the response variable and the average points scored and the average relative skill as predictor variables. This regression model will help your coach predict how many games your team might win in a regular season based on metrics like the average points scored and average relative skill. This model is more practical because you expect more than one performance metric to determine the total number of wins in a regular season. Create this multiple regression model. Make the following edits to the code block below: 1. Replace ??RESPONSE_VARIABLE?? with the variable name that is being predicted. See the table included in the Project Three instructions above. Do not enclose this variable in quotes. For example, if the variable name is var0 then replace ??RESPONSE_VARIABLE?? with var0. 2. Replace ??PREDICTOR_VARIABLE_1?? with the variable name for average points scored. Hint: See the table included in the Project Three instructions above. Do not enclose this variable in quotes. For example, if the variable name is var1 then replace ??PREDICTOR_VARIABLE_1?? with var1. 2. Replace ??PREDICTOR_VARIABLE_2?? with the variable name for average relative skill. Hint: See the table included in the Project Three instructions above. Do not enclose this variable in quotes. For example, if the variable name is var2 then replace ??PREDICTOR_VARIABLE_2?? with var2. For example, if the variable names are var0 for the response variable and var1, var2 for the predictor variables, then the expression in the code block below should be: model = smf.ols(var0 ~ var1 + var2', nba_wins_df).fit() After you are done with your edits, click the block of code below and hit the Run button above. In [10]: import statsmodels. formula. api as smf # Multiple Regression # - --- TODO: make your edits here --- model2 = smf. ols( 'total_wins ~ avg_pts + avg_elo_n', nba_wins_df). fit() print(model2. summary ( ) ) 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: Sat, 18 Jun 2022 Prob (F-statistic): 4.41e-243 Time : 22 :51 : 11 Log-Likelihood: -1904.6 No. observations: 618 AIC: 3815 . of Residuals: 615 BIC: 3829. of Model Covariance Type: nonrobust coef std err P> |+| TO. 025 0.975] Intercept -152.5736 4.500 33.903 . 000 161 .411 143.736 avg_pts 0. 3497 0. 048 7. 297 0.000 0.256 0.444 avg_elo_r 0. 1055 0.002 47.952 3.000 3.101 3. 110 Omnibus : 39 . 087 Durbin-Watson: 1. 203 Prob (Omnibus ) : 0. 090 Jarque-Bera (JB): 160.540 Skew: 3.869 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