Question: A sports-equipment researcher was interested in the relationship between the speed of a golf club…

A sports-equipment researcher was interested in the relationship between the speed of a golf club (in feet per second) and the distance a golf ball travels (in yards). Information was collected on several golfers and was used to obtain the regression equation \( \hat{y} = 2x - 106 \), where \( x \) represents the club speed and \( \hat{y} \) is the predicted distance. What is the predicted distance of a ball that is hit with a club speed of 168 ft/sec?

• 106 yards
• 137 yards
• 230 yards
• 336 yards

Solution

The problem involves finding the predicted distance of a golf ball when hit with a club speed of 168 ft/sec, using the regression equation \( y = 2x - 106 \). First, substitute \( x = 168 \) into the equation to find \( y \). \[ y = 2(168) - 106 \] Calculate \( 2 \times 168 \). \[ 2 \times 168 = 336 \] Subtract 106 from 336. \[ 336 - 106 = 230 \] The predicted distance is 230 yards.