14. Consider the regression below. If X 2 increases by 20 and X 4 decreases by 2

Question

14.   Consider the regression below. If X2 increases by 20 and X4 decreases by 20, what change in Y is predicted by the regression?

     Y=11+10X1+9X2+8X3+7X4+8X5 +u, n=21, R2=0.5

Chapter 7 – Hypothesis Tests and Confidence Intervals in Multiple Regression

15. Consider the coefficients in the excel output above. Directly on that output, put * (5%), or put ** (1%), or put nothing, next to the coefficients (to the left is okay) to indicate the statistical significance.

16. Consider the regression above. What hypothesis is the F-test testing? What is the calculated F-statistic value and what is the p-value of the test? How many degrees of freedom (restrictions) are involved?

17. Read the F-test table to answer this question: With 10 numerator degrees of freedom (restrictions) and using infinity as the denominator degrees of freedom, and an F-statistic of 2.00, what is the best (lowest) level of significance that can be claimed, 10%, 5%, 1%, or none?

Regression Statistics Multiple R. 0.621710238 RSquare 0.386523619 Adjusted R Sqr 0.354235389 Standard Error 0.023185571 Observations 81 ANOVA Regression Residual Total df SS MSF MS F. Significance F | 4 0.025741116 0.006435279 11.97103752 1.35482E-07 76 0.040855372 0.000537571 80 0.066596488 Coefficients Standard Error t Stat p-value Lower 95% Upper 95% Intercept |-0.00373753 0.003201149 -1.167558932 0.246634719 -0.01011317 0.00263811 XVariable 1 0.400460457 0.064363094 6.221895677 2.46285E-08 0.272270245 0.528650668 x Variable 2 0.122804571 0.066456806 1.847885542 0.068509664 -0.009555629 0.255164771 XVariable 3 0.223508923 0.066416449 3.36526455 0.001201362 0.0912291 0.355788746 XVariable 4 0.097599067 0.065999717 1.478780084 0.143332017 -0.033850761 0.229048895

Explanation / Answer

(14)

In regression equation,

Coefficient of X2 = 9, meaning if X2 rises (falls) by 1 unit, Y rises (falls) by 9 units.

As X2 increases by 20 units, Y increases by (20 x 9) = 180 units.

Coefficient of X4 = 7, meaning if X4 rises (falls) by 1 unit, Y rises (falls) by 7 units.

As X4 decreases by 20 units, Y decreases by (20 x 7) = 140 units.

Net increase in Y = Increase due to rise in X2 - Decraese due to fall in X4 = 180 - 140 = 40

NOTE: As per Chegg answering guidelines, 1st question is answered.

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