Question 1: (10 marks in total)

Use the data of 1999 and 2000 only to estimate the next linear model and answer the associated questions below.

SP = 1 + 2 Age + u, (1)

where u is an error term.

Note that the sub-index i of each variable has been suppressed in the above equation.

SP = Selling Price, which is a function of Age (in years).

1.

(a). Generate the descriptive statistics for SP and Age (i.e., 2 VARIABLES IN TOTAL), and report them in a table. (1 point)

(b). Plot SP (y-axis) against Age (x-axis). Do you observe any pattern? (1 point)

2. Estimate the model (1) for the houses sold in Stockton California.

(a). Write down the estimated model (including estimates of the coefficients and the associated standard deviations), and comment on the estimation result using Goodness of fit. (2 points 1 points for reporting the results properly, and 1 point for commenting on Goodness of fit correctly)

(b).Plot the estimated error terms, and calculate the mean squared errors (i.e., 1 N PN i=1 ub 2 i ).

(2 points 1 point for plotting, and 1 point for mean squared errors)

3. At the 5% significance level, test if Age has NEGATIVE impacts on SP. Keep two decimals for the calculation involved. (4 points)

Question 2: (10 marks in total)

Use the data of 2001 only to estimate the next linear model and answer the associated questions below.

log(SP) = 1 + 2 Baths + u, (2)

where u is an error term.

Note that the sub-index i of each variable has been suppressed in the above equation.

1.

(a). Generate the descriptive statistics for log(SP) and Baths (i.e., 2 VARIABLES IN TOTAL), and report them in a table. (1 point)

(b). Plot log(SP) (y-axis) against Baths (x-axis). Do you observe any pattern? (1 point)

2. Estimate the model (2) for the houses sold in Stockton California.

(a). Write down the estimated model (including estimates of the coefficients and the associated standard deviations), and comment on the estimation result using Goodness of fit. (2 points 1 points for reporting the results properly, and 1 point for commenting on Goodness of fit correctly)

(b). Plot the estimated error terms, and calculate the mean squared errors (i.e., 1 N PN i=1 ub 2 i ). (2 points 1 point for plotting, and 1 point for mean squared errors)

3. At the 5% significance level, test if Baths has POSITIVE impacts on log(SP). Keep two decimals for the calculation involved. (4 points)