Question

3. United Park City Properties real estate investment firm took a random sample of five condominium units that recently sold in the city. The sales prices Y (in thousands of dollars) and the areas X (in hundreds of square feet) for each unit are as follows     (40 points)

       

Y= Sales Price ( * $1000)	36	80	44	55	35
X = Area (square feet) (*100)	9	15	10	11	10

The owner wants to forecast sales on the basis of the area. Which variable is the dependent variable? Which variable is the independent variable?

Determine the regression equation.

Interpret the values of the slope and the intercept.

Test the significance of the slope at 1% level of significance.

Determine the coefficient of correlation between the sales price and the area.

Interpret the strength of the correlation coefficient.

Determine the coefficient of determination and present its interpretation.

Determine the coefficient of non-determination.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.969217713
R Square	0.939382976
Adjusted R Square	0.919177301
Standard Error	5.284339356
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1298.227	1298.227	46.49105	0.006453
Residual	3	83.77273	27.92424
Total	4	1382
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-34.5	12.61619	-2.73458	0.071664	-74.6503	5.650339	-74.6503	5.650339
Area	7.681818182	1.126625	6.818434	0.006453	4.096395	11.26724	4.096395	11.26724

Answer 1

a) Sales price is dependent and Area is independent

b) Y'= -34.5+7.681818182*Area

c) To interpret coeffciients:

For every additional unit of area, Sales price increases by 7.6818182 units.

At zero Area, the minimum sales price is -34.5 units.

d) Hypothesis test:

and

The test statistic:

P-value: 0.006453

The test statistic is significant and rejects H0. There is sufficient evidence to support the claim that there is a significant relationship between two variables.

e) The correlation coefficient between two variables: r= 0.969217713

f)The correlation coefficient is strong with positive trend. To be strong r value>0.80.

h) Coefficient of determination(R-sqaured):  0.939382976

The proportion of variation explained by regression equation is 0.939382976.

i) Unexplained varition= 1- R-sqaured value= 1- 0.939382976= 0.06061702

The proportion of variation unexplained by regression equation is 0.06061702