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)
What are the endpoints of the interval estimator for $\beta$ ₂ with a 95% interval estimate?

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)
What are the endpoints of the interval estimator for

\beta

₂ with a 95% interval estimate?

Quizplus · Accepted Answer

The endpoints of the interval estimator for the slope coefficient (β1) with a 95% confidence interval can be calculated using the estimated coefficient plus or minus the critical value from the t-distribution (which depends on the desired level of confidence and the degrees of freedom) times the standard error of the estimate. Given the slope coefficient estimate of 33.74 and its standard error of 9.42, and knowing we are looking for a 95% confidence interval (which typically involves a t-value that would result in an interval wider than just one standard error due to the sample size and desired confidence level), the only plausible option provided that reflects a reasonable range around the estimate given its standard error is (14.90, 52.58). This range is wide enough to account for the variability indicated by the standard error and the level of confidence desired.

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

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