Question

A high-school administrator who is concerned about the amount of sleep the students in his district are getting selects a random sample of 14 seniors in his district and asks them how many hours of sleep they get on a typical school night. He then uses school records to determine the most recent grade-point average (GPA) for each student. Here is the regression output. Assume the conditions for inference are met. 1.

Predictor Coef SE Coef T P
Constant 2.6476 0.3281 8.07 0.000
Sleep 0.10176 0.04347 **** *****

S = 0.1804
R-Sq = 31.3%
R-Sq(adj) = 25.6%

Required:
Predict the GPA for a senior in this district who gets 8 hours of sleep on a typical school night.

Answer 1

3.46

Explanation:

Given the regression output :

Predictor Coef ___SE __ Coef __ T ___ P

Constant 2.6476_0.3281_ 8.07 0.000

Sleep 0.10176 0.04347 **** *****

S = 0.1804

R-Sq = 31.3%

R-Sq(adj) = 25.6%

The regression equation which models the relationship between hours of sleep a student gets and his GPA can be obtained from the regression output :

The GPA is the dependent, y variable

Hours of sleep is the independent, x variable

y = 0.10176x + 2.6476

Hence, the GPA of a student who gets 8 hours of sleep on a typical school can be computed thus ;

Hours of sleep, x = 8

y = 0.10176(8) + 2.6476

y = 0.81408 + 2.6476

y = 3.46168

Thus, predicted GPA = 3.46