Chapter 3.2, Problem 46E

To determine

To find andinterpret: the residuals for the month.

Answer to Problem 46E

The residual is -13.032 and its negative; this shows the data point lies below the line.

Explanation of Solution

Given:

During March, the average temperature was $\text{46}{\text{.4}}^{0}F$ and Joan used 490 cubic feet of gas per day.

Calculation:

Consider the case how much gas; in this case “Temperature (X)” will help explain “Gas consumed (Y)”. So “Temperature (X)” is the explanatory variable and “Gas consumed (Y)” is the response variable. Regression line is given as:

  $\widehat{Y}=1425-19.87X$

Predicted gas consumed to maintain the temperature $\text{46}{\text{.4}}^{0}F$ ,$\begin{array}{l}\widehat{Y}=1425-19.87X\\ =1425-19.87\left(46.4\right)\\ =503.032\end{array}$

Predicted gas consumed to maintain the temperature $\text{46}{\text{.4}}^{0}F$ is 503.032 cubic feet and actual (observed) gas consumed to maintain the temperature $\text{46}{\text{.4}}^{0}F$ was 490 cubic feet.

  $\begin{array}{l}\text{residual = observed Y}-\text{predectedY}\\ \text{ = Y}-\text{<mover accent="true"><mo>Y</mo><mo>^</mo></mover>}\\ \text{ = 490}-\text{503}\text{.032}\\ \text{ =}-13.032\end{array}$

Conclusion:

Hence, this residuals is negative; this shows the data point lies below the line.