Refer to hprice1 dataset (see "Course Resources" in "Modules" → "Welcome to Class: Your Journey Begins Here!"). Use Excel’s regression data analysis tool or Stata to compute the answers to the questions asked. Consider the following regression model: price = β0 + β1lotsize + β2sqrft + β3bdrms + u, where price is house price in $1,000s, lotsize is size of lot in square feet, sqrft is size of house in square feet and bdrms is number of bedrooms. The heteroskedasticity-robust standard error you obtain for β^2{\widehat\beta}_2 is [Fill in the blank],
. Let α = 5%. You further estimate whether the size of house is statistically different from zero, using the heteroskedasticity-robust t statistic; your conclusion is [Fill in the blank],
.

NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. For your second answer, write either YES or NO.

HINT: See Example 8.1.

Question

Refer to hprice1 dataset (see "Course Resources" in "Modules" → "Welcome to Class: Your Journey Begins Here!"). Use Excel’s regression data analysis tool or Stata to compute the answers to the questions asked. Consider the following regression model: price = β0 + β1lotsize + β2sqrft + β3bdrms + u, where price is house price in $1,000s, lotsize is size of lot in square feet, sqrft is size of house in square feet and bdrms is number of bedrooms. The heteroskedasticity-robust standard error you obtain for β^2{\widehat\beta}_2  is [Fill in the blank],
.  Let α = 5%. You further estimate whether the size of house is statistically different from zero, using the heteroskedasticity-robust t statistic; your conclusion is [Fill in the blank],
.

NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. For your second answer, write either YES or NO.

HINT: See Example 8.1.

BlackTom AI · Accepted Answer

This question asks you to supply two blanks based on a regression analysis: (1) the heteroskedasticity-robust standard error for beta2-hat (the coefficient on sqrft), and (2) a yes/no decision on whether the size of the house is statistically different from zero using a heteroskedasticity-robust t statistic, at α = 5%.

First, note that to fill these blanks you must compute them from the actual dataset (hprice1) using either Excel’s regression data analysis tool or Stata, and then report the results in a very specific format. The model is price = β0 + β1(lotsize) + β2(sqrft) + β3(bdrms) + u, where price is in thousands of dollars, lotsize in square feet, sqrft is house size in square feet, and bdrms is the number of bedrooms. The requested standard error is the robust (heteroskedasticity-robust) standard error of β2-hat, which is typically denoted se(β2̂) or SE(β2̂) in the output produced by either software when you request robust standard errors (often labeled as robust or HC1 in Stata, or homoskedasticity-robust in Excel).

Important conceptual steps for the first blank:
- Run the regression with price on the right-hand side including lotsize, sqrft, and bdrms as regressors.
- Request heteroskedasticity-robust standard errors for the coefficient estimates. In Stata, this is typically packages or options that produce robust standard errors (e.g., reg price lotsize sqrft bdrms, robust). In Excel, you may compute robust SEs manually or use software that provides HC1-type SEs when you enable robust standard errors. 
- Locate the standard error corresponding to the coefficient on sqrft (β2̂). Write this numeric value with two decimal places, including the required formatting (leading minus sign if negative, leading zero before the decimal if necessary, thousands separators if applicable). If the SE is, for example, 12.3456, you would report 12.35, and if negative SEs were ever shown (they aren’t in standard outputs for standard errors), you’d use the absolute value; but standard errors are nonnegative.

Important conceptual steps for the second blank:
- Use the heteroskedasticity-robust t statistic for testing H0: β2 = 0. This t statistic is t_robust = β2̂ / se(β2̂), where β2̂ is the OLS (or robust) estimate of the coefficient on sqrft and se(β2̂) is the robust standard error you retrieved in the first step. 
- Compare the absolute value of t_robust to the critical value from a t-distribution with the appropriate degrees of freedom under the robust inference framework, or simply compare the p-value to α = 0.05. If |t_robust| > t_(n-k, 0.975) (or if p-value < 0.05), you reject H0 and conclude that the size of the house (sqrft) is statistically different from zero. Otherwise, you fail to reject H0. 
- Since the instruction asks you to answer YES or NO, report YES if you reject H0 at 5% with robust SEs, and NO otherwise.

Data and formatting caveats:
- The prompt requires that the first answer be written in number format with 2 decimal places, and to include a leading minus sign if needed, a leading zero before the decimal, and trailing zeros when appropriate. Since standard errors are nonnegative, the leading minus sign would not apply to the SE value itself. Ensure you present the number with two decimals, e.g., 12.34. 
- The second answer must be either YES or NO, corresponding to whether β2 is statistically different from zero at α = 5% using the robust t statistic. 
- If the dataset or regression output is not provided here, you cannot determine the exact numeric values. In that case, you should run the regression in your software with the specified options, extract the robust SE for β2, compute t_robust = β2̂ / se(β2̂), and determine the conclusion for H0: β2 = 0. Then format the two answers exactly as requested.

In summary, you need to produce two pieces of information from the actual regression output: (1) the robust standard error for the sqrft coefficient, formatted to two decimals, and (2) YES if the robust test rejects that coefficient equals zero at 5% significance, otherwise NO. If you cannot access the hprice1 dataset and run the regression, you must indicate that the specific numeric values cannot be provided from the information given here. It’s essential to perform the analysis with the dataset to fill these blanks accurately.

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