Applications The commercial division of a real estate firm is conducting a regre

Question

Applications The commercial division of a real estate firm is conducting a regression analysis of the relationship between x, annual gross rents (in thousands of dollars), and y, selling price (in thousands of dollars) for apartment buildings. Data were collected on several properties recently sold and the following computer output was obtained. 40. Analysis of Variance SOURCE Regression Error Total DF 1 7 8 Adj SS 41587.3 51984.1 Predictor Constant 20.000 Coef SE Coef T-Value 6.21 5.29 3.2213 1.3626 7.210 Regression Equation Y = 20.0 + 7.21 X How many apartment buildings were in the sample? Write the estimated regression equation. a. b.

Explanation / Answer

Using above output:

a) Sample:

DF total= n-1= 8 => n = 9

Total number of samples= 9

b) Estmated regression equation: Y=b0+b1*X

Y= 20.0+7.21*X

c) Sb1:

Slope of coefficient b1: 1.3626

d) For F-test:

DFRegression=1

DFError= 7

SSRegression= 41587.3

SSTotal= 51984.1

SSError= SST-SSR = 51984.1-41587.3 = 10396.8

MSRegression= SSR/DFR = 41587.3

MSError= SSE /DFE= 1485.257

F= MSR/MSE =28.0007

P-value: 0.001134(Using F table)

The test statistic is significant and rejects H0. Becasue P-value is less than significant level 0.05. There is enough evidence to conlude that there is a significant relationship between variables.

e) X= 55000

Y= 20.0+ 7.1*X

Y= 20+ 7.21* 50 =380.5($1000's)

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