OLS Regression Results R-squared: Adj. R-squared: Dep. Variable: mpg 0.821 Model: OLS 0.808 Method: Least Squares F-statistic: 61.98 Prob (F-statistic): Log-Likelihood: Date: Wed, 07 Oct 2020 8.10e-11 Time: 11:19:54 -70.463 No. Observations: 30 AIC: 146.9 Df Residuals: 27 BIC: 151.1 Df Model: 2 Covariance Type: nonrobust coef std err P>lt| [0.025 0.975] Intercept 37.1838 1.650 22.540 0.000 33.799 40.569 wt -3.8810 0.658 -5.902 0.000 -5.230 -2.532 hp -0.0309 0.010 -3.201 0.003 -0.051 -0.011 Omnibus: 4.159 Durbin-Watson: 2.606 Prob (Omnibus) : 0.125 3.100 Jarque-Bera (JB) : Prob (JB) : Skew: 0.784 0.212 Kurtosis: 3.147 Cond. No. 561. Warnings: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Is at least one of the two variables (weight and horsepower) significant in the model?
![**OLS Regression Results**
- **Dependent Variable:** mpg
- **Model:** OLS (Ordinary Least Squares)
- **Method:** Least Squares
- **Date:** Wed, 07 Oct 2020
- **Time:** 11:19:54
**Statistics:**
- **Number of Observations:** 30
- **Degrees of Freedom (Df) Residuals:** 27
- **Degrees of Freedom (Df) Model:** 2
- **Covariance Type:** nonrobust
**Model Fit:**
- **R-squared:** 0.821
- **Adjusted R-squared:** 0.808
- **F-statistic:** 61.98
- **Prob (F-statistic):** \(8.10 \times 10^{-11}\)
- **Log-Likelihood:** -70.463
- **AIC (Akaike Information Criterion):** 146.9
- **BIC (Bayesian Information Criterion):** 151.1
**Coefficients:**
1. **Intercept:**
- Coefficient: 37.1838
- Standard Error: 1.650
- t-statistic: 22.540
- P-value: 0.000
- 95% Confidence Interval: [33.799, 40.569]
2. **wt (weight):**
- Coefficient: -3.8810
- Standard Error: 0.658
- t-statistic: -5.902
- P-value: 0.000
- 95% Confidence Interval: [-5.230, -2.532]
3. **hp (horsepower):**
- Coefficient: -0.0309
- Standard Error: 0.010
- t-statistic: -3.201
- P-value: 0.003
- 95% Confidence Interval: [-0.051, -0.011]
**Diagnostic Tests:**
- **Omnibus:** 4.159
- **Prob (Omnibus):** 0.125
- **Durbin-Watson:** 2.606
- **Jarque-Bera (JB):** 3.100
- **Prob (JB):** 0.212
- **Skew:** 0.784
- **K](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7c098e8-a055-46a5-964b-ab0cc684192c%2F10ba54c0-6d11-49ca-96e6-3085b38a0741%2Fyaoqis3_processed.png&w=3840&q=75)
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