Question

In Example 2.43 on page 127 , we used the approval rating of a president running for re-election to predict the margin of victory or defeat in the election. We saw that the least squares line is \(\widehat{\text { Margin }}=-36.76+0.839\) ( Approval). Interpret the slope and the intercept of the line in context.

Short answer

The slope of the least squares line is \(0.839\), which means that for each unit increase in the approval rating, the margin of victory or defeat (Margin) is expected to increase by 0.839 units, on average. The intercept of the line is \(-36.76\), which would indicate that when the approval rating is zero, the expected margin of victory or defeat (Margin) is -36.76. However, this interpretation is not realistic as an approval rating of zero is unlikely and falls outside the range of the observed data.

Step-by-step solution

Interpret the Slope

The slope of the line is \(0.839\). This is interpreted as for each increase of one unit in the approval rating, the margin of victory or defeat (Margin) is expected, on average, to increase by 0.839 units.

Interpret the Intercept

The intercept of the line is \(-36.76\). This is interpreted as when the approval rating is zero, the expected margin of victory or defeat (Margin) is -36.76. However, this interpretation may not make sense in the given context, as an approval rating of zero is unrealistic in this scenario and thus falls outside the range of the observed data.