Suppose the classical linear regression model applies to y=a+Bx+yw+0z+ Where x, w, z are independent variables,...

 

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Suppose the classical linear regression model applies to y=a+Bx+yw+0z+ Where x, w, z are independent variables, & is the error term, and a,ß,y, and 0 are parameters to be estimated with OLS. a. What regression is necessary to incorporate true information that ß-20? Be as specific as you can. b. If the restriction is true, will the restricted regression you propose in (a) have a larger or smaller R2? Explain. c. Use your intuition to answer this question: will the variance of 0 be bigger or smaller with the new regression? Explain. d. Will the estimate of be biased in the restricted regression if the information is false? e. Explain exactly what you would do to test your regression in (a) against the unrestricted regression. Show the null and alternative hypothesis, what type of test you would perform, and the degrees of freedom for the numerator and denominator. Hint: For b, c, and d: you need to write just a few sentences, thinking about "truth" (unbiasedness) and "precision" (smallest variance). You do not need to add any equations to the answers to b,c, and d. Suppose the classical linear regression model applies to y=a+Bx+yw+0z+ Where x, w, z are independent variables, & is the error term, and a,ß,y, and 0 are parameters to be estimated with OLS. a. What regression is necessary to incorporate true information that ß-20? Be as specific as you can. b. If the restriction is true, will the restricted regression you propose in (a) have a larger or smaller R2? Explain. c. Use your intuition to answer this question: will the variance of 0 be bigger or smaller with the new regression? Explain. d. Will the estimate of be biased in the restricted regression if the information is false? e. Explain exactly what you would do to test your regression in (a) against the unrestricted regression. Show the null and alternative hypothesis, what type of test you would perform, and the degrees of freedom for the numerator and denominator. Hint: For b, c, and d: you need to write just a few sentences, thinking about "truth" (unbiasedness) and "precision" (smallest variance). You do not need to add any equations to the answers to b,c, and d.

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