Dep. Variable: Model: Method: Date: Time: No. Observations: Df Residuals: Df Model: OLS Regression Results total_wins R-squared: OLS Least Squares Fri, 13 Oct 2023 09:43:01 618 615 2 Adj. R-squared: Prob (F-statistic): F-statistic: Log-Likelihood: AIC: BIC: 0.837 0.837 1580. 4.41e-243 -1904.6 3815. 3829.

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a) What is the equation for this model? b) What are the null hypothesis, alternative hypothesis, and the level of significance? c) What is the test statistic and the p-value?
Certainly! Below is the transcription of the OLS Regression Results as it might appear on an educational website, with detailed explanations of the components:

---

### OLS Regression Results

**Dependent Variable:**  
- **total_wins**

**Model Information:**  
- **Model:** OLS (Ordinary Least Squares)
- **Method:** Least Squares
- **Date:** Fri, 13 Oct 2023
- **Time:** 09:43:01

**Observations and Degrees of Freedom:**  
- **Number of Observations:** 618
- **Degrees of Freedom Residuals:** 615
- **Degrees of Freedom Model:** 2

**Covariance Type:**  
- nonrobust

**Summary of Results:**

|                | coef     | std err | t       | P>|t|    | [0.025    | 0.975]   |
|----------------|----------|---------|---------|--------|------------|----------|
| Intercept      | -152.5736 | 4.500   | -33.993 | 0.000  | -161.411   | -143.736 |
| avg_elo_n      | 0.1055    | 0.002   | 47.952  | 0.000  | 0.101      | 0.110    |
| avg_pts        | 0.3497    | 0.048   | 7.297   | 0.000  | 0.256      | 0.444    |

**Statistical Measures:**

- **R-squared:** 0.837  
  Indicates that 83.7% of the variance in the dependent variable can be explained by the model.

- **Adjusted R-squared:** 0.837  
  This value adjusts the R-squared for the number of predictors in the model.

- **F-statistic:** 1580.  
  This tests the overall significance of the model.

- **Prob (F-statistic):** 4.41e-243  
  The probability that the observed F-statistic would occur by chance. A very low value indicates a significant model.

- **Log-Likelihood:** -1904.6  
  A measure of model fit; higher values indicate a better fit.

- **AIC (Akaike Information Criterion):** 3815.  
  Used for model selection
Transcribed Image Text:Certainly! Below is the transcription of the OLS Regression Results as it might appear on an educational website, with detailed explanations of the components: --- ### OLS Regression Results **Dependent Variable:** - **total_wins** **Model Information:** - **Model:** OLS (Ordinary Least Squares) - **Method:** Least Squares - **Date:** Fri, 13 Oct 2023 - **Time:** 09:43:01 **Observations and Degrees of Freedom:** - **Number of Observations:** 618 - **Degrees of Freedom Residuals:** 615 - **Degrees of Freedom Model:** 2 **Covariance Type:** - nonrobust **Summary of Results:** | | coef | std err | t | P>|t| | [0.025 | 0.975] | |----------------|----------|---------|---------|--------|------------|----------| | Intercept | -152.5736 | 4.500 | -33.993 | 0.000 | -161.411 | -143.736 | | avg_elo_n | 0.1055 | 0.002 | 47.952 | 0.000 | 0.101 | 0.110 | | avg_pts | 0.3497 | 0.048 | 7.297 | 0.000 | 0.256 | 0.444 | **Statistical Measures:** - **R-squared:** 0.837 Indicates that 83.7% of the variance in the dependent variable can be explained by the model. - **Adjusted R-squared:** 0.837 This value adjusts the R-squared for the number of predictors in the model. - **F-statistic:** 1580. This tests the overall significance of the model. - **Prob (F-statistic):** 4.41e-243 The probability that the observed F-statistic would occur by chance. A very low value indicates a significant model. - **Log-Likelihood:** -1904.6 A measure of model fit; higher values indicate a better fit. - **AIC (Akaike Information Criterion):** 3815. Used for model selection
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