Problem Quants- Confidence Interval
Question from the curriculum:
Selected Regression Output - Dependent Variable: Amtex Share Return
Intercept 0.0095 ( coefficient ); 0.0078 ( standard error)
Oil return 0.2354 ( coefficient ); 0.0760 ( standard error)
( Note: The critical t-value for a one-sided t-test at the 5% significance level
28. Vasileva should compute the:
A coefficient of determination to be 0.4689.
B 95% confidence interval for the intercept to be –0.0037 to 0.0227.
C 95% confidence interval for the slope coefficient to be 0.0810 to 0.3898.
The correct answer is C while I got B because I have used a df of 35 ( 36 total number of observations) and significance level of 5% ( t= 1.691 as shown above).
Thus, I did this for the confidence interval: 0.0095+ 1.691 ( 0.0078) = 0.22682 ( upper level) and 0.0095-1.691 (0.0078)= -0.003682 (lower level)
C is correct. The confidence interval for the slope coefficient is calculated as:
Where b1 0.2354, sb1= 0.0760 and tc = 2.032
The lower limit for the confidence interval = 0.2354 – (2.032 × 0.0760) = 0.0810
The upper limit for the confidence interval = 0.2354 + (2.032 × 0.0760) = 0.3898
I don’t get it ; where is this 2.032 coming from and why are they not using 1.691 if it was given?
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