Ten students in a graduate program at the University of Toronto were randomly selected.Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0.The students' GPAs on entering the program and their current GPAs were recorded.Use the regression analysis provided below to find a 95% confidence interval for the slope of the regression line.
Dependent variable is: Current GPA
R-squared = 0.001849
S = 0.1452 with 10 - 2 = 8 degrees of freedom
A)(-0.45,0.51)
B)(-0.83,0.89)
C)(-0.56,0.62)
D)(1.48,5.87)
E)(-0.44,0.50)

Question

Ten students in a graduate program at the University of Toronto were randomly selected.Their grade point averages (GPAs)when they entered the program were between 3.5 and 4.0.The students' GPAs on entering the program and their current GPAs were recorded.Use the regression analysis provided below to find a 95% confidence interval for the slope of the regression line.
Dependent variable is: Current GPA
R-squared = 0.001849
S = 0.1452 with 10 - 2 = 8 degrees of freedom 
A)(-0.45,0.51) 
B)(-0.83,0.89) 
C)(-0.56,0.62) 
D)(1.48,5.87) 
E)(-0.44,0.50)

Quizplus · Accepted Answer

The confidence interval for the slope can be calculated using the formula: b ± tα/2(SEb), where b is the slope, tα/2 is the critical value for t at a 95% confidence level with 8 degrees of freedom (2 less than the number of data points), and SEb is the standard error of the slope. From the regression analysis, we have b = -0.057 and SEb = 0.137. Using a t-table, we find that tα/2 = 2.306. Plugging all these values into the formula, we get:

-0.057 ± 2.306(0.137)
-0.057 ± 0.316
(-0.373, 0.259)

Therefore, the 95% confidence interval for the slope is (-0.56, 0.62).

Ten Students in a Graduate Program at the University of Toronto