Math Problem Statement

OLS Regression Results

Dep. Variable: total_wins R-squared: 0.823 Model: OLS Adj. R-squared: 0.823 Method: Least Squares F-statistic: 2865. Date: Thu, 12 Dec 2024 Prob (F-statistic): 8.06e-234 Time: 17:16:20 Log-Likelihood: -1930.3 No. Observations: 618 AIC: 3865. Df Residuals: 616 BIC: 3873. Df Model: 1
Covariance Type: nonrobust

             coef    std err          t      P>|t|      [0.025      0.975]

Intercept -128.2475 3.149 -40.731 0.000 -134.431 -122.064 avg_elo_n 0.1121 0.002 53.523 0.000 0.108 0.116

Omnibus: 152.822 Durbin-Watson: 1.098 Prob(Omnibus): 0.000 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.

Solution

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Math Problem Analysis

Mathematical Concepts

Regression Analysis
Ordinary Least Squares (OLS)
Statistical Significance
Multicollinearity

Formulas

Linear Regression Formula: Y = β0 + β1X + ε
R-squared = 1 - (SS_res / SS_tot)
t-statistic = (Coefficient - Hypothesized Value) / Standard Error

Theorems

Gauss-Markov Theorem
Central Limit Theorem (assumption for normality of residuals)

Suitable Grade Level

Undergraduate Statistics/Graduate Level