Question

Mr. Ledford is concerned about the amount of sleep the students in his district are getting. He 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. His regression output along with a residual plot and a histogram of the residuals are given below.
Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8
GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7

Required:
Do these data provide convincing evidence of a linear relationship between the hours of sleep students typically get and their academic performance, as measured by their GPA?

Answer 1

Answer:

Hence, the data provides convincing evidence that a linear relationship exists between hours of sleep observed and academic performance as measured by GPA.

Step-by-step explanation:

Given the data:

Sleep (hrs) 9 8.5 9 7 7.56 7 5.5 6 8.5 6.5 8

GPA 3.8 3.3 3.5 3.6 3.4 3.3 3.2 3.2 3.2 3.4 3.6 3.1 3.4 3.7

The scatter plot shows a positive linear trend. With the correlation Coefficient depicting a R value of 0.56. The residual plot also depicts a a randomly scattered values of the residual values. Similarly, a plot of the normal values of  residuals