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.

Please provide correct answer without using excel formula. Thanks.

Answer 1

X :- Player Height (cm)

Y :- Free Throw Shooting Percentage

ΣX = 1594
ΣY = 6.36
ΣX * Y = 1263.29
ΣX2 = 318110
ΣY2 = 5.0992

Part a)

r = -0.845

Coefficient of Determination
= 0.714
Explained variation = 0.714* 100 = 71.4%
Unexplained variation = 1 - 0.714* 100 = 28.6%

71.4% of variation in Free Throw Shooting is explained by Player Height.

Part b )

Equation of regression line is Ŷ = a + bX


b = -0.008
a =( Σ Y - ( b * Σ X) ) / n
a =( 6.36 - ( -0.0078 * 1594 ) ) / 8
a = 2.348
Equation of regression line becomes Ŷ = 2.348 - 0.008 X

Part c)

When X = 200
Ŷ = 2.348 + -0.008 X
Ŷ = 2.348 + ( -0.008 * 200 )
Ŷ = 0.75