In class we covered the basics of multiple linear regression. It differs from chapter 3’s linear regression because it has more predictors. The simple linear regression formula is \[\hat{y_i}= \hat{\beta_0}+\hat{\beta_1} x_1\]. With multiple linear regression the regression fomula simply grows to include more beta-i’s and xi’s. For example with two predictors the model would be \[\hat{y_i}= \hat{\beta_0}+\hat{\beta_1} x_1+\hat{\beta_2}x_2\].
We also covered the Sum of Squared Residuals (SSE) and Mean Squared Error (MSE) for multiple linear regression. SSE= the sum of (yi-yhati)^2 and MSE= SSE/[n-(k+1)]. We also learned about the Multiple Coefficient of Determination denoted R^2. This is found by dividing the explained variation by the total variation, explained variation = [sum of (yhati-ybar)^2]/[sum of (yhati-ybar)^2 + sum of (yi-yhati)^2].We also learned that adjusted R^2 penalizes for bad predictors where as R^2 does not.
Next we covered F-statistic. We learned that as df1 increases, the F distribution is stretched to the right. When df2 decreases, the distribution is compressed vertically.
Lastly we talked about indicator variables or dummy variables. These variables take on a 0 or 1 value. Indicator variables are a way to measure qualitative variables.