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IQ_cat is a new, categorical variable that divides IQ into q…

IQ_cat is a new, categorical variable that divides IQ into quartiles. In other words, 1 indicates the respondent is in the bottom quarter of the distribution, 2 indicates the respondent is between the 25th and 50th percentile, 3 indicates the respondent is between the 50th and 75th percentile, and 4 indicates the respondent is in the top quarter of the distribution (so, those in category 4 are the “smartest”, assuming you trust IQ tests). You are interested in whether there is a relationship between IQ quartile and whether the respondent lives in a metro area as the first step in a broader analysis of the distribution of employees across different locations. So, you run the following in Stata: State the null and alternative hypotheses for this chi-square test.

You decide to substitute the continuous IQ variable for a se…

You decide to substitute the continuous IQ variable for a series of dummy variables indicating quartiles. IQ_1= 1 if the respondent is in the bottom quarter of the distribution, IQ_2=1 if the respondent is between the 25th and 50th percentile, IQ_3=1 if the respondent is between the 50th and 75th percentile, and IQ_4=1 if the respondent is in the top quarter of the distribution (so, the IQ_1 people are the “dumbest” and the IQ_4 people are the “smartest”, again, assuming you trust IQ tests). You re-run the regression and get the following output: Which of all the statistically significant coefficients (not just the IQ variables) has the largest association with wage? How do you know? 

Now, you decide to run the original regression, except using…

Now, you decide to run the original regression, except using the natural log of wage as the dependent variable. You get the following: Interpret the coefficient on educ (again, just say in words what the coefficients means; do not worry about practical significance).