Use the data in housingdata.xls to answer the following questions. (a) Consider a simple linear regression model
Question:
(b) Now, consider a multiple linear regression model: price = α0 + α1sqrf t + α2bdrms + α3lotsize + v
i. Estimate this model by OLS and interpret the estimated effects of number of bedrooms (bdrms) and size of lot (lotsize) on house price (price). Are these two variables statistically significant at the 5% significance level?
ii. Test H0 : α2 = α3 against a two-sided alternative. Do you reject H0 at the 5% significance level? iii. Is the estimated effect of sqrf t on price substantially different from the regression that excludes bdrms and lotsize? Does the regression in (a) seem to suffer from omitted variable bias? Explain.
iv. Explain why se(βˆ 1) can be smaller or greater than se( ˆα1). [se stands for standard errors] (c) Now, estimate the following two linear regression models price = γ0 + γ1sqrf t + γ2lotsize + w lotsize = κ0 + κ1sqrf t + z 2 Assignment
2 i. What is the variance inflation factor for the slope coefficients in the first model?
Do you think there is little, moderate or strong collinearity between sqrf t and lotsize? ii. Show that βˆ 1 = ˆγ1 + ˆγ2κˆ1 where βˆ 1 is the estimated coefficient of sqrf t on price (comes from question(a)).
Introductory Econometrics A Modern Approach
ISBN: 978-0324660548
4th edition
Authors: Jeffrey M. Wooldridge