Plotting selling price and age in a x-­y scatter plot

Question

This assignment data file contains 1500 houses sold in Stockton, California, during1996-­-1998.

The variable descriptions are as follows:

• Sprice = Selling price of home, dollars

• Livarea = living area, hundreds of square feet

• Age = age of home at time of sale, years

• Baths = number of bathrooms

• Beds = number of bedrooms

• Pool = 1 if home has pool, 0 otherwise

• Lgelot =1 if lot size > 0.5 acres, 0 otherwise.

Model 1:

Sprice = δ₁ +δ₂livarea+ δ₃Age+ δ₄Beds+δ₅Baths + e

Model 2:

Sprice =β₁ + β₂livarea + β₃age + β₄Beds+ β₅Baths + β₆livarea² + β₇age²+ ε

Model 3:

ln Sprice = α₁ + α₂livarea + α₃livarea²+ α₄age+ α₅age² + α₆Beds+ ε ln=natural log

Question1) Plot each of Sprice and Age in a X-­-Y scatter plot and comment on their pattern.

(To obtain XY scatter plot in Gretl choose “View” and “Graph specified vars” and “X-­-Y scatter” and select the variables to the relevant boxes)

Model 1

Question2) Estimate Model 1 and report results. Do the signs of the estimates agree with your expectations? Describe.

Question3) Using Model1, test null hypothesis that each individual coefficient is equal to zero against alternative that it is not, at the 5% significance level and comment on your findings

Question4) Consider two houses that have the living areas of the same size, same number of bathrooms, and same number of bedrooms, but one is two years old and the other is ten years old. How much difference in the prices must an investor expect between two houses according to Model 1? Construct a 95% confidence interval for this difference in the prices and interpret your result

Question5) Test overall significance of the model at the 1% significance level. Interpret the test result.

Question6) A family of four children owns a house with a living area of 2,000 square feet (i.e. Livarea = 20). They are now considering an extension of living area by 200 square feet. How much will this extension be expected to increase price of the house? Test a hypothesis, at the 5% significance level, that increase in the price would be equal to $20,000 against it is more than $20,000.

Model 2

Question7) Estimate Model 2 and use an F-­- test to test that Livearea² and Age² are significant variables in the model? Use the 5% significance level and comment on your results.

Model 3

Question8) Estimate Model 3 and comment on your results.

Question9) Use Model 3 to predict the price of a 10-­-year-­-old house with a living area of 2,000 square feet, and three bedrooms. Comment on your answer

Models 2 and 3

Question10) Compare the results of Model 2 and Model 3 and select a preferred model. Give reasons for your choice.