Question

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:                                                                                   

2. Calculate the estimated regression line.   [3 marks]
   
   
   
   
3. What is the meaning of the slope? Interpret it using the words of the problem. [1 marks]

4. Predict the selling price (point estimate) for a house with an appraised value of $200,000. [1 marks]

5. Interpret r² using the words of the problem. [1 marks]
   

6. 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]

Answer 1

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.

Please upvote. Thanks in advance.