Making Predictions from a Least-Squares Regression Line — Quiz
Question 10 • Statistical Reasoning
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 widehat y is equal to 2 x minus 106 , where x represents the club speed and widehat y is the predicted distance. Which statement best describes the meaning of the slope of the regression line?
Answer
A
For each increase in club speed by 1 ft/sec, the predicted distance increases by 2 yards.
B
For each increase in distance by 1 yard, the predicted club speed decreases by 106 ft/sec.
C
For each increase in distance by 1 yard, the predicted club speed increases by 2 ft/sec.
D
For each increase in club speed by 1 ft/sec, the predicted distance decreases by 106 yards.
Explanation
In the regression equation ŷ = 2x − 106, the slope is 2. Since x is club speed in feet per second and ŷ is predicted distance in yards, the slope means that for each 1 ft/sec increase in club speed, the predicted distance increases by 2 yards. The −106 is the intercept, not the slope.
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