- Multiple linear regression is a generalization to simple linear regression
**One**Response v.s.**multiple**predictors- $y=\beta_0+\beta_1x_1+\beta_2x_2+\cdots+\beta_px_p+\varepsilon$

- A convenient way to draw scatterplots for many variables
- Each cell is a scatterplot for the two corresponding variables

- Model summary
- Coefficients

- ANOVA

- Drop insignificant variables
- $R^2$ not decreasing much
- Before:
**0.581**; After:**0.575**

- Before:
- Std. error not increasing much
- Before:
**0.93273**; After:**0.93478**

- Before:

- Using the regression equation to do prediction

$\hat{y}=0.302+1.151*Var1+0.155*Var2$

- Residual = True value - predicted value
- Look into original data to find the true value
- Use the predicted value above