A linear regression model was built to predict the housing price (dependent variable) using thefollowing independent variables (predictors):

renovated_no: =1 if the house was not renovated, =0 otherwise; zipcode_98003: =1 house is located in zipcode 98003, =0 otherwise; zipcode_98007: =1 house is located in zipcode 98007, =0 otherwise; bedrooms: Number of bedrooms; bathrooms: Number of bathrooms; lot: Land space, which is converted using z-transformation; sqft_above: The square footage of the interior housing space above ground level; sqft_basement: The square footage of the interior housing space below ground level;

The model specification for the house price (dependent variable) is: House price = 426967.904 - 128559.094 renovated_no +82677.643 zipcode_98003 - 101088.776 zipcode_98007 + 56967.721 bedrooms + 8016.794 bathrooms + 69800 lot + 198.285 sqft_above+ 128.592 sqft_basement

Assume all predictors are significant. Based on the information above, answer the following questions. Show the steps how you obtain the result for all questions below for full credits.

(1) For two houses: house A is located in zip code 98003 and was not renovated, and house B islocated in zip code 98007 but was renovated, assuming the other conditions of the twohouses are the same, which one has the higher expected price and what is the difference? Show the steps how you obtain the result.

(2) For two houses: house A has 2,000 sqft interior space above ground and 1,050 sqft basementand house B has 1,800 sqft interior space and 1,200 sqft basement, assuming the otherconditions of the two houses are the same, which one has the higher expected price and whatis the difference? Show the steps how you obtain the result.

(3) The coefficient of variable "lot" is 69800, what is the interpretation of this coefficient?

(4) When a house has a value of 0 for the variable "lot", what does it mean? Can a house have anegative value for the variable "lot" and why or why not?