Question

# Mabel, a real estate agent, is looking for a method of predicting the selling prices of...

1. Mabel, a real estate agent, is looking for a method of predicting the selling prices of houses in Burnaby. Since the City of Burnaby appraises houses for the purpose of assessing taxes, she investigates a small sample of recently sold houses to see if there is a linear relationship between the appraised value and the selling price. Her data is in this table:
 Appraised Value (\$1,000’s) Selling Price (\$1,000’s) 250 257 190 250 220 288 185 162 270 285 500 541 240 221

The Excel regression output is shown below, with two cells missing.

 Regression Statistics Multiple R 0.955 R Squared 0.912 Adjusted R Squared 0.895 Standard Error 39.055 Observations 7.000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 41.771 0.115 0.9127 -102.560 112.191 Appraised Value (\$1,000’s) 0.147 7.203 0.0008 0.683 1.441
1. What is the independent variable, and what is the dependent variable? [1 marks]

Independent Variable:

Dependent Variable:

1. Calculate the estimated regression line.   [3 marks]

2. What is the meaning of the slope? Interpret it using the words of the problem. [1 marks]
1. Predict the selling price (point estimate) for a house with an appraised value of \$200,000. [1 marks]
1. Interpret r2 using the words of the problem. [1 marks]

1. Test at the 5% level of significance (95% level of confidence) if there is a linear relationship between the appraised value and the selling price in population by 4 approaches:

t crit / t test: [2 Mark]

p-value/alpha:      [1 mark]

confidence interval:    [1 marks]

Ftest/Fcrit: [2 marks]

a)

independent variable = Appraised Value (\$1,000’s)

dependent value = Selling Price

Y = 41.771 + 0.147 * X

.

b)

slope = 0.147

so, if increase the appraised value by 1 unit, then selling price will be increase by 0.147

..........

c)

for X = 200

y = 41.771 + 0.147*200

=71.171

..

R Squared = 0.912

so, 91.2% of data is explained by independent variable appraised value of selling price

.................

t stat = 7.203

t critical = 2.571

t stat > t critical, slope significant

p value = 0.0008 >0.05 , slope significant

lower limit = 0.683 , upper limit = 1.441

CI does not contain 0 , slope is significant

................

Please revert back in case of any doubt.

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