In the first two problems, we want to examine whether a transformed variable can produce better regression results based on OLS assumptions and requirements.

1. Open the wage1.dta dataset using the following command:
   1. bcuse wage1

1. Provide univariate summary statistics for wageand its log transformation, lwage.
   1. Tip: do a log-transformed variable, you would use the command:
      1. gen logvar = log(var)

1. Estimate the following equation:
   1. wage_i = ₀ + ₁(educ_i) + ₂(exper_i) + ₃(tenure_i) + u_i

1. Save the residuals and plot a histogram
   1. To save residuals as a variable "r", follow these steps:
      1. reg var1 var2 var3
      2. predict r, resid

1. Repeat part (i), but with lwage as the dependent variable.

1. Would you say that Assumption MLR.6 is closer to being satisfied for the level-level model or the log-level model

1. Use the housing price data in HPRICE1 for this exercise.
   1. bcuse hprice1

1. Estimate the following model and report the results in the usual OLS format.
   1. log(price_i) = ₀ + ₁(log(lotsize_i)) + ₂(log(sqrft_i)) + ₃(bdrms_i) + u_i

1. Find the predicted value of log(price) , when lotsize= 20,000, sqrft = 2,500, and bdrms = 4. Using the methods in Section 6-4, find the predicted value of price at the same values of the explanatory variables.

1. For explaining variation in price, decide whether you prefer the model from part (i) or the model:
   1. price_i = ₀ + ₁(lotsize_i) + ₂(sqrft_i) + ₃(bdrms_i) + u_i

The final question asks you to consider the effects of binary 'dummy' variables in your regression.

1. Use the data in WAGE2 for this exercise.
   1. bcuse wage2

1. Estimate the following model and report the results in the usual form:
   1. Log(wage_i) = ₀ + ₁(educ_i) + ₂(exper_i) + ₃(tenure_i) + ₄(married_i) + ₅(black_i) + ₆(south_i) + ₇(urban_i) + u_i

1. What is your interpretation of the coefficients on married, black, south,and urban?

1. Holding other factors fixed, what is the approximate difference in monthly salary between blacks and non-blacks? Is this difference statistically significant?

1. What is the estimated wage differential between married blacks and married non-blacks?

1. What is the estimated wage differential between non-married black urban southerners, and married non-black non-southerners?