Chapter 4.2, Problem 4.52E

(a)

To determine

To explain how well does the regression line fit the data and also give numerical and graphical evidence to support the answer.

Explanation of Solution

Graphical:

The residuals are all centered about zero and the regression line fits the data well.

Numerical:

The square of the correlation ${\text{r}}^2$ is the fraction of variation in the values of y that is explained by the least square regression of $y\text{ on }x$ .

Thus, we then know that $96\%$ of the variation is explained by the regression line and thus the regression line fits the data well.

(b)

To determine

To compare the temperature predictions for the least square line and this formula.

Explanation of Solution

We note that this new formula gives values that are relatively close to the old formula. The first two values are underestimated and the other two values are overestimated.