Refer to given Exercise about y = foot length and x = height. (Data source: the height foot dataset on the companion website.) If the person who reportedly is 84 inches tall is excluded, the regression equation for the remaining 32 men is y^ = 0.25 + 0.384x.
a. How much does average foot length increase for each 1-inch increase in height?
b. Predict the difference in the foot lengths of men whose heights differ by 10 inches.
c. Suppose Max is 70 inches tall and has a foot length of 28.5 cm. On the basis of the regression equation, what is the predicted foot length for Max? What is the value of the prediction error (residual) for Max?
Exercise
The heights (inches) and foot lengths (cm) of 33 college men are shown in the following table. (These data are in the dataset height foot on the companion website.)
a. Draw a scatterplot with y = foot length (cm) and x = height (inches). Does the relationship appear to be linear? Are there any outliers? If so, do you think the outliers are legitimate data values?
b. Use statistical software or a calculator to calculate the correlation between height and foot length. If heights were converted to centimeters, what would be the correlation between height and foot length?
c. If there are any outliers, remove them and recalculate the correlation. Describe how the correlation changed from part (b).