Question

The following table shows the number of wins eight teams had during a football season. Also shown are the average points each team scored per game during the season. Construct a​ 90% prediction interval to estimate the number of wins for teams that scored an average of 27 points a game.

Points_per_Game	Wins
25.3	12
18.7	6
20.6	5
24.6	9
12.5	2
22.4	7
22.7	12
23.7	9

Answer 1

ΣX = 170.5 ΣY = 62 ΣX * Y = 1407.7 ΣX2 = 3754.29
Sxx =Σ (Xi - X̅ )2 = 120.50875
Syy = Σ( Yi - Y̅ )2 = 83.5
Sxy = Σ (Xi - X̅ ) * (Yi - Y̅) = 86.325

X̅ = Σ (Xi / n ) = 170.5/8 = 21.3125
Y̅ = Σ (Yi / n ) = 62/8 = 7.75

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2 )
b = ( 8 * 1407.7 - 170.5 * 62 ) / ( 8 * 3754.29 - ( 170.5 )2)
b = 0.7163

a =( ΣY - ( b * ΣX ) ) / n
a =( 62 - ( 0.7163 * 170.5 ) ) / 8
a = -7.517
Equation of regression line becomes Ŷ = -7.517 + 0.7163 X

Predictive Confidence Interval of
Ŷ = -7.517 + 0.7163 X
Ŷ = 11.8231

t(α/2) = t(0.1/2) = 1.943
X̅ = (Xi / n ) = 170.5/8 = 21.3125


90% Predictive confidence interval is ( 7.4657 < < 16.1826 )