• Residual degrees of freedom = Sample size n - model size k -1
• Adjusted $R^2$ is always greater than $R^2$.

Calibration Plot

Scatterplot between actual values of Y and expected values of Y

Marginal Slope

slope of explanatory variable in Simple Linear Regression

Partial Slope

slope of explanatory variable in multiple linear regression excluding the effect of other explanatory variables

Path Diagram

schematic drawing of the relationships among the explanatory variables and the response

Interpretation of Regression Output

If p-value is less than alpha value, reject the null hypothesis (regression is not significant)

Variance Inflation Factor

<aside> 💡 quantifies the amount of unique variation in each explanatory variable and measures the effect of collinearity

</aside>

$$ VIF(X_j) = \frac{1}{1-R_j^2} $$

$R_j^2$ is coefficient of determination in the regression of $X_j$ on all of the other explanatory variables

• Larger the VIF, larger is collinearity
• Large VIF can substantially increase the standard error in predicting the partial slopes making those predictions unreliable