Question 3: Log-transformations and Multiple Regression. Suppose that you have a theory that specifies: @AM°Se Tw Y and you want to estimate parameters 8, 6, 4, and w. (a) Transform this equation into a form that we could estimate with OLS. (b) Suppose that you estimated your regression in Stata. The program estimates coefficients and standard errors, then presents p-values and other things that help you assess significance. But what kind of test did Stata run to generate the p-values? What are the null and alternative hypotheses? Is the test one-tailed or two tailed? Why might this matter? (c) Suppose that your theory specifies that should be close to 0.5. How could you test whether or not this was true in your data? (d) Now suppose that instead our theory specifies that 8 + 8 + = 1 and that 0= w. How would you test whether or not this was true in your data?

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Question 3: Log-transformations and Multiple Regression.
Suppose that you have a theory that specifies:
@AM®S*€
Tw
Y =
and you want to estimate parameters 8, 8, 4, and w.
(a)
Transform this equation into a form that we could estimate with OLS.
(b) Suppose that you estimated your regression in Stata. The program
estimates coefficients and standard errors, then presents p-values and other
things that help you assess significance. But what kind of test did Stata run to
generate the p-values? What are the null and alternative hypotheses? Is the test
one-tailed or two tailed? Why might this matter?
(c) Suppose that your theory specifies that should be close to 0.5. How could
you test whether or not this was true in your data?
(d) Now suppose that instead our theory specifies that 0 + 8 + 4 = 1 and that
0 = w. How would you test whether or not this was true in your data?
Transcribed Image Text:Question 3: Log-transformations and Multiple Regression. Suppose that you have a theory that specifies: @AM®S*€ Tw Y = and you want to estimate parameters 8, 8, 4, and w. (a) Transform this equation into a form that we could estimate with OLS. (b) Suppose that you estimated your regression in Stata. The program estimates coefficients and standard errors, then presents p-values and other things that help you assess significance. But what kind of test did Stata run to generate the p-values? What are the null and alternative hypotheses? Is the test one-tailed or two tailed? Why might this matter? (c) Suppose that your theory specifies that should be close to 0.5. How could you test whether or not this was true in your data? (d) Now suppose that instead our theory specifies that 0 + 8 + 4 = 1 and that 0 = w. How would you test whether or not this was true in your data?
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