You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates) : y = 97.25 + 33.74* x
(3) 86) (9.42)
You want to test the following hypothesis: H₀: $\beta$ ₂ = 12,H1: $\beta$ ₂≠12.If you choose to reject the null hypothesis based on these results,what is the probability you have committed a Type I error?

Question

You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates) : y = 97.25 + 33.74* x
(3) 86) (9.42)
You want to test the following hypothesis: H₀:

\beta

₂ = 12,H1:

\beta

₂≠12.If you choose to reject the null hypothesis based on these results,what is the probability you have committed a Type I error?

Quizplus · Accepted Answer

To test the hypothesis we need to calculate the t-statistic as follows:
t = (b1 - 12)/SE(b1) = (33.74 - 12)/9.42 = 2.26
where b1 is the coefficient estimate, 12 is the hypothesized value of the coefficient, and SE(b1) is the standard error of the coefficient estimate.
The degrees of freedom for this test are df = n - k = 60, where n is the sample size and k is the number of variables in the model (excluding the intercept). 
Using a two-sided t-test at the 5% significance level, we have a critical value of ±2.002 for df = 60. 
Since our calculated t-statistic of 2.26 exceeds the critical value of 2.002, we reject the null hypothesis. 
The probability of committing a Type I error is the significance level, which is 5%. Therefore, the answer is C.

You Estimate a Simple Linear Regression Model Using a Sample β\betaβ

You Estimate a Simple Linear Regression Model Using a Sample $\beta$