Exam 7: Hypothesis Tests and Confidence Intervals in Multiple Regression

Consider the regression model Yi = β0 + β1X1i + β2X2i+ β3X3i + ui.Use "Approach #2" from Section 7.3 to transform the regression so that you can use a t-statistic to test: β1 =

The homoskedasticity-only F-statistic is given by the following formula

Your textbook has emphasized that testing two hypothesis sequentially is not the same as testing them simultaneously.Consider the following confidence set below,where you are testing the hypothesis that H0 : β5 = 0,β6 = 0. Your statistical package has also generated a dotted area,which corresponds to drawing two confidence intervals for the respective coefficients.For each case where the ellipse does not coincide in area with the corresponding rectangle,indicate what your decision would be if you relied on the two confidence intervals vs.the ellipse generated by the F-statistic.

Using the 420 observations of the California School data set from your textbook,you estimate the following relationship: = 681.44 - 0.61LchPct n=420,R2=0.75,SER=9.45 where TestScore is the test score and LchPct is the percent of students eligible for subsidized lunch (average = 44.7,max = 100,min = 0). a.Interpret the regression result. b.In your interpretation of the slope coefficient in (a)above,does it matter if you start your explanation with "for every x percent increase" rather than "for every x percentage point increase"? c.The "overall" regression F-statistic is 1149.57.What are the degrees of freedom for this statistic? d.Find the critical value of the F-statistic at the 1% significance level.Test the null hypothesis that the regression R2= 0. e.The above equation was estimated using heteroskedasticity robust standard errors.What is the standard error for the slope coefficient?

Let R2unrestricted and R2restricted be 0.4366 and 0.4149 respectively.The difference between the unrestricted and the restricted model is that you have imposed two restrictions.There are 420 observations.The F-statistic in this case is