Calculate R-Squared

Now that you've calculated the RMSE of your model's predictions, you will examine how well the model fits the data: that is, how much variance does it explain. You can do this using $R^2$.

Suppose $y$ is the true outcome, $p$ is the prediction from the model, and $res = y - p$ are the residuals of the predictions.

Then the total sum of squares $tss$ ("total variance") of the data is:

$$ tss = \sum{(y - \overline{y})^2} $$

where $\overline{y}$ is the mean value of $y$.

The residual sum of squared errors of the model, $rss$ is: $$ rss = \sum{res^2} $$

$R^2$ (R-Squared), the "variance explained" by the model, is then:

$$ 1 - \frac{rss}{tss} $$

After you calculate $R^2$, you will compare what you computed with the $R^2$ reported by glance(). glance() returns a one-row data frame; for a linear regression model, one of the columns returned is the $R^2$ of the model on the training data.

The data frame unemployment is in your workspace, with the columns predictions and residuals that you calculated in a previous exercise.

The data frame unemployment and the model unemployment_model are in the workspace.

Calculate the mean female_unemployment and assign it to the variable fe_mean.
Calculate the total sum of squares and assign it to the variable tss.
Calculate the residual sum of squares and assign it to the variable rss.
Calculate $R^2$. Is it a good fit ($R^2$ near 1)?
Use glance() to get $R^2$ from the model. Is it the same as what you calculated?

Exercise

Calculate R-Squared

Instructions