Question

Consider the following Excel outout for a regression model where Y = GDP, X, employment and Xx = fixed capital Sample size = 20 observations Intercept Standard Error 34370.0541 5.8749 0.0962 Coefficients 59450 2848 12.3387 0.4346 Pour 0.1064 Star 17049 2.1003 Lower 95% -133019.7674 -0.0562 Upper 95% 14118.9979 2 4.7336 00003 Model 1: Y = Bo+B.X1+B2X:+8 Based on the value of statistic, determine whether you should reject or not to reject the null hypothesis of two failed test). Make decision at 0.05. Model 1: Y = Bo + B1X1 + B2X2 + € Based on the value of 95% confidence intervals, determine whether you should reject or not to relect the null hypothesis of 25 (two tailed test). Make decision at a = 0.05. SUMMARY OUTPUT Based on the p-value determine whether you should reject or not to reach the nw hypothesis of B:- 0 (two tailed test). Make decision at a = 0,05 Regression Statistics Multiple R 0.9883 R Square 0.9768 Adjusted R Square 0.9741 Standard Error 13445.4057 Observations Conduct hypothesis testing B2 = 0.5 againts By 0.5 at a = 0.05. Test for overall significance of all slope coefficients at x = 0.05. 20

Answer 1

a. Since p-value = 2P(t > 2.1003t -t20-3) = 0.0509 > 0.05 so we fail to reject null hypothesis at 5% level of significance and conclude that Biis insignificantly different from zero. 6. Value of t = (0.4346 – 0.25)/0.0962 = 1.9189 Since p-value = 2P(t > 1.9189|t t17) = 0.0719 > 0.05 so we fail to reject null hypothesis at 5% level of significance and conclude that B, is insignificantly different from 0.25. c. Value of t = 0.4346/0.0962 = 4.5177 Since p-value = 2P(t > 4.5177t t17) = 0.0003 < 0.05 so we reject null hypothesis at 5% level of significance and conclude that B, is significantly different from 0. d. Value of t= (0.4346 – 0.5)/0.0962 = -0.6798 Since p-value = 2P(t > 0.6798|t t17) = 0.5058 > 0.05 so we fail to reject null hypothesis at 5% level of significance and conclude that B2 is insignificantly different from 0.5.

e. Value of F= 122 17 D2X = 357.8793 p - value = P(F > 357.8793|F ~ F2,17) = 0.0000 < 0.05 so overall regression equation is significant.