# 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.

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