Question

Using the data in the StudentSurvey dataset, we use technology to find that a regression line to predict weight (in pounds) from height (in inches) is \(\widehat{\text { Weigh }} t=-170+4.82(\) Height \()\) (a) What weight does the line predict for a person who is 5 feet tall ( 60 inches)? What weight is predicted for someone 6 feet tall ( 72 inches)? (b) What is the slope of the line? Interpret it in context. (c) What is the intercept of the line? If it is reasonable to do so, interpret it in context. If it is not reasonable, explain why not. (d) What weight does the regression line predict for a baby who is 20 inches long? Why is it not appropriate to use the regression line in this case?

Short answer

Predicted weight for 5 feet tall person is 118 pounds and for 6 feet tall person is 176.84 lbs. The slope is 4.82, meaning for each one inch increase in height, weight increases by 4.82 pounds. The intercept is -170, but it doesn't have a valid interpretation. As for a baby of 20 inches, the model predicts negative weight (-26.6 lbs), making it inappropriate in this context.

Step-by-step solution

Prediction for 5 feet and 6 feet tall person

Using the regression equation, \(\widehat{\text { Weight }}=-170+4.82(\text { Height })\), we need to substitute the heights in inches, i.e., 60 inches, and 72 inches respectively. For 60 inches, it will be \(\widehat{\text { Weight }}=-170+4.82( 60) = 118 lbs\) and for 72 inches, \(\widehat{\text { Weight }}=-170+4.82( 72) = 176.84 lbs\).

Slope Interpretation

The slope of the regression line is 4.82. It means, for each increase of one inch in height, the model predicts an increase in weight of approximately 4.82 pounds.

Intercept Interpretation

The Y-intercept of the line is -170, which represents the predicted weight for a person with zero height. However, this is practically impossible and not reasonable, so there is no valid interpretation in this context.

Prediction for a baby

For a baby of 20 inches height, the regression line predicts \(\widehat{\text{Weight}}=-170+4.82( 20) = -26.6 lbs\). This is obviously not reasonable as weight can’t be negative. Therefore, it is not appropriate to apply this regression line for babies because the original data set didn’t apply to babies and thus, it doesn’t fit well within the infants' height-weight proportionality.