In the first two problems, we want to examine whether a transformed variable can produce better regression results based on OLS assumptions and requirements Open the wage1 dta dataset using the following command bcuse wage1 Provide univariate summary statistics for wage and its log transformation, lwage Tip do a log transformed variable, you would use the command gen logvar log(var) Estimate the following equation wage i 0 1 (educ i ) 2 (exper i ) 3 (tenure i ) u i Save the residuals and plot a histogram To save residuals as a variable r , follow these steps reg var1 var2 var3 predict r, resid Repeat part (i), but with lwage as the dependent variable Would you say that Assumption MLR 6 is closer to being satisfied for the level level model or the log level model Use the housing price data in HPRICE1 for this exercise bcuse hprice1 Estimate the following model and report the results in the usual OLS format log(price i ) 0 1 (log(lotsize i )) 2 (log(sqrft i )) 3 (bdrms i ) u i 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 For explaining variation in price, decide whether you prefer the model from part (i) or the model 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 Use the data in WAGE2 for this exercise bcuse wage2 Estimate the following model and report the results in the usual form 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 What is your interpretation of the coefficients on married, black, south, and urban Holding other factors fixed, what is the approximate difference in monthly salary between blacks and non blacks Is this difference statistically significant What is the estimated wage differential between married blacks and married non blacks What is the estimated wage differential between non married black urban southerners, and married non black non southerners

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on May 19, 2024

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

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

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

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)

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

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

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

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

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

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

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.

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.

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

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

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

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