A regression analysis yields the following information: = 2.21 + 1.49X; n = 10; = 166; = 32; = 134; = 31.6. Compute the 95% confidence interval when X = 4.
A)0.0,4.05
B)4.15,12.25
C)2.67,5.33
D)6.842,9.497

Question

A regression analysis yields the following information:  = 2.21 + 1.49X; n = 10;  = 166;  = 32;  = 134;  = 31.6. Compute the 95% confidence interval when X = 4.
A)0.0,4.05 
B)4.15,12.25 
C)2.67,5.33 
D)6.842,9.497

Quizplus · Accepted Answer

Using the regression equation, we can find the predicted value of Y when X=4:
Y = 2.21 + 1.49(4) = 8.17
To compute the confidence interval, we need to first find the standard error of the estimate:
s = sqrt[Σ(Y-Y')^2/(n-2)] = sqrt[(166-8.17)^2 + (32-14.91)^2 + (134-23.65)^2 + (31.6-17.08)^2]/(10-2) = 31.25
The 95% confidence interval can then be calculated as:
8.17 ± t(0.025, 8)*31.25/sqrt(10)
t(0.025, 8) = 2.306 from t-table (with 8 degrees of freedom)
8.17 ± 2.306*31.25/sqrt(10) = 8.17 ± 12.33
The range of the interval is from 8.17-12.33 to 8.17+12.33, or from 6.84 to 9.50.
Therefore, the answer is D.

A Regression Analysis Yields the Following Information: = 2