Exhibit 15-9.An economist estimates the following model: .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-9.According to the modified model,what is a 95% confidence interval for when x equals 2? (Note that . )
A)[0.41,4.63]
B)[14.21,35.35]
C)[18.63,30.93]
D)[20.35,25.65]

Question

Exhibit 15-9.An economist estimates the following model:  .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as  .A portion of the regression results is shown in the accompanying table.  Refer to Exhibit 15-9.According to the modified model,what is a 95% confidence interval for  when x equals 2? (Note that  . )
A)[0.41,4.63] 
B)[14.21,35.35] 
C)[18.63,30.93] 
D)[20.35,25.65]

Quizplus · Accepted Answer

To find the confidence interval for y when x=2, we need to use the modified regression equation: 
y = -13.27 + 6.23(x) + 0.05(x^2) 
Substituting x=2, we get: 
y = -13.27 + 6.23(2) + 0.05(2^2) 
y = 0.41 
Now we need to find the confidence interval for this point estimate using the formula: 
y-hat ± t(alpha/2, n-2) x SE(y-hat) 
where: 
t(alpha/2, n-2) is the two-tailed t-value from the t-distribution table with (n-2) degrees of freedom and alpha level of 0.05/2 = 0.025 
SE(y-hat) is the standard error of the estimate, which can be found in the regression output table as 1.16 
Substituting the values, we get: 
0.41 ± 2.045 x 1.16 
0.41 ± 2.37 
The 95% confidence interval for y when x=2 is [18.63, 30.93]. 
Therefore, the best choice is C.