Question

Taller basketball players have a theoretical shooting advantage because it’s harder to block them. But can a player’s height determine how well they shoot free throws, where there is no defender?

Player Height (cm)	Free Throw Shooting Percentage
198	80%
196	74%
201	83%
198	85%
188	91%
191	84%
214	68%
208	71%

a) Determine the coefficient of determination and interpret its value.

b) What is the equation of the regression line? Keep three decimal places for calculated values.

c) Estimate the percentage of free throws a 200cm tall player will make.

Answer 1

a) Correlation (Using Excel function CORREL( ) ) = CORREL(player height, free throw) = -0.845

Coefficient of determination = -0.845^2 = 0.714

71.4% of variation in free throw shooting percentage is explained by player height.

b) y = ax+b

a (Using Excel function SLOPE(y,x)) = SLOPE(free throw, player height) = -0.008

b (Using Excel function INTERCEPT(y,x)) = INTERCEPT(free throw, player height) = 2.348

y = 2.348 - 0.008x

c) Player height = 200cm

Percentage of free throws = 2.348 - 0.008*200 = 0.748 = 74.8%