Problem: You have run a regression with 500 observations to explain house prices. Among your explanatory variables are square footage and number of bedrooms. Their estimated slopes are 1.2 and 50, respectively, measured in hundreds of dollars. Their estimated variances are 0.04 and 225, and their estimated covariance is 2. You are contemplating adding a 150 square foot bedroom to your house.
a)By how much do you estimate this addition would increase the value of your house?
b)What is the variance of this estimate (var )?
c)What is its 95% confidence interval?