You have collected data for the 50 U.S. states and estimated the following relationship between the change in the unemployment rate from the previous year ( $\widehat{\Delta u r}$ ) and the growth rate of the respective state real GDP (g_y) . The results are as follows $\widehat{\Delta u r}$ = 2.81 - 0.23 $\times$ g_y, R²= 0.36, SER = 0.78 (0.12) (0.04)
Assuming that the estimator has a normal distribution, the 95% confidence interval for the slope is approximately the interval

Question

You have collected data for the 50 U.S. states and estimated the following relationship between the change in the unemployment rate from the previous year (

\widehat{\Delta u r}

) and the growth rate of the respective state real GDP (g_y) . The results are as follows

\widehat{\Delta u r}

= 2.81 - 0.23

\times

g_y, R²= 0.36, SER = 0.78 (0.12) (0.04)
Assuming that the estimator has a normal distribution, the 95% confidence interval for the slope is approximately the interval

Quizplus · Accepted Answer

The 95% confidence interval for the slope coefficient (-0.23) is calculated using the standard error of the estimate (0.04) and the critical value for a 95% confidence level from the normal distribution (approximately 1.96). The interval is computed as -0.23 ± 1.96*0.04, which results in approximately [-0.31, -0.15].

You Have Collected Data for the 50 U Δur^\widehat{\Delta u r}Δur

You Have Collected Data for the 50 U $\widehat{\Delta u r}$