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

The task presents a regression model: price = β0 + β1 lotsize + β2 sqrft + β3 bdrms + u, where price is in thousands of dollars. We are asked to fill two blanks: (1) the heteroskedasticity-robust standard error for β̂2, and (2) whether the size of the house (sqrft) is statistically different from zero using the heteroskedasticity-robust t statistic, with a 5% significance level.

First, consider what the heteroskedasticity-robust standard error (often denoted as SERobust(β̂2)) represents. It adjusts the usual OLS SE to be valid under heteroskedasticity, typically using the sandwich (White) estimator or a similar robust covariance estimator. The exact numeric value depends on the sample data (n, X, residuals) from the hprice1 dataset. In this specific prompt, the provided answer for the first blank is 0.02, which would be the robust standard error attached to the coefficient on sqrft when you run the regression in either Excel (regression data analysis) or Stata with heteroskedasticity-robust options.

Now, turning to hypothesis testing for β2 using the robust t statistic. The null hypothesis here is H0: β2 = 0. The robust t statistic is tRobust = β̂2 / SERobust(β̂2). You compare |tRobust| to the critical value from the t distribution with appropriate df (often using a robust degrees-of-freedom adjustment). If the absolute value of the statistic exceeds the critical value (or the p-value is below 0.05), you reject H0 and conclude that sqrft has a statistically significant association with price.

In the provided answer, the second blank is YES, meaning the conclusion is that the size of the house (sqrft) is statistically different from zero at the 5% level using the heteroskedasticity-robust t test. This implies that, given the sample data and the robust standard error of 0.02 for β̂2, the computed t statistic satisfies either |tRobust| > critical value (around 2.0 for large samples at 5% two-sided test) or the p-value is less than 0.05, leading to rejection of H0: β2 = 0.

To interpret the numeric formatting guidance: the instruction says to write the first answer in number format with 2 decimal places, including a leading minus sign if negative, and proper thousands separators. The value 0.02 already matches two decimals and positive form. If you were to report it, you would present it exactly as 0.02. For the second item, reporting YES indicates significance at the 5% level.

In practical steps, if you were reproducing this: you would run the regression price on lotsize, sqrft, and bdrms, request heteroskedasticity-robust standard errors (e.g., in Stata: regress price lotsize sqrft bdrms, robust; in Excel: use the robust option if available or implement White's estimator via a plugin or add-in), extract the SE for β̂2, verify it equals 0.02 to two decimals, then compute t = β̂2 / 0.02 and check whether |t| exceeds the critical value for your df (or check the p-value) at the 5% level. The prompt’s given answers reflect that sequence: SERobust(β̂2) = 0.02 and H0: β2 = 0 is rejected (YES).

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