Assignment 4

  1. Consider the data given in the Problem 1 of Assignment 3. Under the model

yi = β0 + β1xi1 + β2xi2 + β3 xi3 + β4xi4 + β5xi5 + `i ,

where i = 1, K, n and ` = (`1, K,`n )T ~ N (0,m2In),

(a) find a 95% C.I. for β1.

(b) find a 95% C.I. for β3 + 2β5.

  1. Suppose a person has a house to sell in the area, from which the data were gathered. The variables in the data set are:

PRICE: selling price of house in thousands of dollars
BDR: number of bedrooms
FLR: floor space in sq. ft. (computed from dimensions of each room and then augmented by 10%)
FP: number of fireplaces
RMS: number of rooms
ST: storm windows (1 if present, 0 if absent)
LOT: front footage of lot in feet
TAX: annual taxes
BTH: number of bathrooms
CON: construction (0 if frame, 1 if brick)
GAR: garage size (0=no garage, 1=one-car garage, etc.)
CDN: condition (1="needs work", 0 otherwise)
L1: location (L1=1 if property is in zone A, L1=0 otherwise)
L2: location (L2=1 if property is in zone B, L2=0 otherwise)

The house for selling has 750 square feet of space, 5 rooms, 2 bedrooms, 1.5 baths, storm windows, a 1-car garage, 1 fireplace and a 25 front-foot lot. What can you tell him about how much he could expect to get for the house? Please report your fitted model and also construct a confidence interval for the prediction.