PLEASE use R and show in detail the codes. Problem # 2: Residential sales that o

Question

PLEASE use R and show in detail the codes.

Problem # 2: Residential sales that occurred during the year 2005 were available from a city in the Midwest. Data on 50 arms-length transactions include sales price (y in thousand), finished square feet (x1, in thousand), number of bedrooms (x2), lot size (x3, in thousand), year built (x4, consider 2005=50), distance from a popular highway (x5, in mile). The city tax assessor was interested in predicting sales price based on the demographic variable information given above. The data have not produced here. However, the Splus output are provided below.

Coefficients:

..................Value ...........Std Error .......t value .......Pr( > | t | )

(Intercept) 314.1311 ......143.5370 .....2.1885 ........0.0340

x1 ............0.0291 ...........0.0142 .........2.0496 ........0.0464

x2 ...........16.7504 ..........7.5896 ..........2.2070 ........0.0326

x3 ...........1.9283 ............3.1550 ...........0.6112 ........0.5442

x4.......... - 1.9159 ............2.4940 .....  - 0.7682 .........0.4465

x5........... - 5.1714 ............2.0729 ........- 2.4948 ........0.0164

Residual Standard error: 89.77 on 44 degrees of fredom.

Multiple R-Squared: 0.7266

F-statistic: 23.390 on 5 and 44 degrees of fredom, the p-value is 0.0000

Correlation of Coefficients:

(Intercept) x1 x2 x3 x4

x1 -0.6466

x2 -0.5736 0.0299   

x3 -0.4838 0.2660 0.3397

x4 -0.1646 -0.0746 0.1487 0.2737

x5 -0.1623 -0.0625 0.0732 -0.0571 -0.2684

(a) Determine the multiple regression equation for the residential sales data.

(b) Suppose you do not know the p-values, find the best predictor for Y.

(c) Interpret the coefficient of determination, R2.

(d) Estimate the sale price of a house whose finished square feet is 2500 (square

feet), 4 bedrooms, 5500 sq feet lot size, built in 2000 and 20 miles far from high way.

(e) Estimate the sale price of a house whose finished square feet is 2500 (square

feet), 4 bedrooms, 7500 sq feet lot size, built in 2000 and 20 miles far from high way. Compare results in (d) and (e).

(f) At the 5% significance level, does it appear that any of the predictor variables can be

removed from the full model as unnecessary?

(g) Obtain and interpret 99% confidence intervals for the coefficient 3.

(h) Test the hypothesis that H0: 2 + 5=9, versus H1: 2 + 5>9. Use =0.02.

Explanation / Answer

Please note that this is an interpretation question , no R codes are needed

a) the regression equation can be formed using the coefficients as

sales = 314.1311 + 0.0291x1 + 16.7504x2 +1.9283x3 -1.9159x4 -5.17x5

c) the coefficient of determination is 0.7266. This means the model is able to explain 72.66% variation in the value of sales due to variation in the independent variables from x1 to x5

d)
using the regression equation and putting the values we get

sales = 314.1311 + 0.0291x1 + 16.7504x2 +1.9283x3 -1.9159x4 -5.17x5

sales = 314.1311 + 0.0291*2500 + 16.7504*4 +1.9283*5500 -1.9159*45 -5.17*5 = 10947.46

e)

using the regression equation and putting the values we get

sales = 314.1311 + 0.0291x1 + 16.7504x2 +1.9283x3 -1.9159x4 -5.17x5

sales = 314.1311 + 0.0291*2500 + 16.7504*4 +1.9283*7500 -1.9159*45 -5.17*5 = 14804.06

f)
check the p values of all the variables from the output table , all variabes whose p value is less than 0.05 are considered signficant , other variables can be dropped from the model

x3 and x4 are not signficant for the model

please note that we can answer only 4 subparts of a question at a time , as per the answering guidelines

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