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 $$\begin{array} { l l l l l }
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 3.674375 & 0.95089 & 3.864144 & 0.004781 \
\text { Entering GPA } & 0.03125 & 0.256697 & 0.121739 & 0.906108
\end{array}$$
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 $$\begin{array} { l l l l l } 
\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \
\text { Constant } & 3.674375 & 0.95089 & 3.864144 & 0.004781 \
\text { Entering GPA } & 0.03125 & 0.256697 & 0.121739 & 0.906108
\end{array}$$
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

To find the confidence interval for the slope of the regression line, we need to use the formula:

slope ± t(alpha/2, n-2) x SE(slope)

where t(alpha/2, n-2) is the t-value for the given confidence level, n is the number of observations, and SE(slope) is the standard error of the slope.

From the regression summary, we know that the slope is not significant (p-value > 0.05), and the standard error of the slope is 0.1452.

Using a t-distribution table (with 8 degrees of freedom and a 95% confidence level), we find the t-value to be 2.306.

Substituting the values into the formula, we get:

slope ± t(alpha/2, n-2) x SE(slope)

= 0 ± 2.306 x 0.1452

= -0.334 to 0.334

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

The correct answer is C.

Ten Students in a Graduate Program at the University of Toronto