Listed below are STATA results where y is regressed on a constant, x1 x2 x3, usi

Question

Listed below are STATA results where y is regressed on a constant, x1 x2 x3, using 24 observations. This question asks you to fill in some of the blank results.

Using Panel A, answer the following questions:

i. Construct a 95% confidence interval for the parameter on x1 by hand.

ii. Using a t-test, test the null hypothesis H0 : B1 = 0 vs H1 : B1 does not equal 0 at 5% level. Can we use the confidence interval of part (i) to reject the null hypothesis that B1 = 0?

iii. How do your results above change if you change the confidence level to 99% and the test significance level to 1%?

In panel B below, we have estimates of a model where y is regressed on x1 and a constant using the same 24 observations.

Panel A reg y x1 x2 x3 df Source I SS MS Model I 407 06 7.668 135 689.223 Residual 938379.666 20 46918.9833 Total I 134 54 47.33 23 58497.7101 y I Coef Std. Err x1 I 34.78137 13.24421 x2 I 8.757655 30.83438 3 I 161071 3664861 cons I 83.06 376 627.1563 P> lt I 24 Number of obs F 13, 20) 2.89 Prob F 0.0608 R-squared 0.3026 Adj R-squared 0.1979 Root MSE 216.61 [95% Conf Interval

Explanation / Answer

Result:

Multiple parts; Panel A answered

Using Panel A, answer the following questions:

95% critical value of t with 20 df is 2.086

Lower limit of 95% CI for slope =34.78137-2.086*13.24421 =7.153948

Upper limit of 95% CI for slope =34.78137+2.086*13.24421 =62.40879

ii. Using a t-test, test the null hypothesis H0 : B1 = 0 vs H1 : B1 does not equal 0 at 5% level. Can we use the confidence interval of part (i) to reject the null hypothesis that B1 = 0?

t=34.78137/13.24421 =2.626157

df for error =20

Critical t at 5% level =2.086

Calculated t=2.626157> critical value 2.086.

Ho is rejected.

Under 5% level ,B1 is significant.

iii. How do your results above change if you change the confidence level to 99% and the test significance level to 1%?

Critical t at 1% level = 2.845

Calculated t=2.626157<critical value 2.845.

Ho is not rejected.

The result changed.

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