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
Y= Sales Price ( * $1000) 
36 
80 
44 
55 
35 
X = Area (square feet) (*100) 
9 
15 
10 
11 
10 
a. The owner wants to forecast sales on the basis of the area. Which variable is the dependent variable? Which variable is the independent variable?
b. Determine the regression equation.
c. Interpret the values of the slope and the intercept.
d. Test the significance of the slope at 1% level of significance.
e. Determine the coefficient of correlation between the sales price and the area.
f. Interpret the strength of the correlation coefficient.
g. Determine the coefficient of determination and present its interpretation.
h. Determine the coefficient of nondetermination.
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 
Pvalue 
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 
a) The dependent variable is Sales price.
The independent variable is Area
b) The regression equation is =  34.5 + 7.681818182*x
c) Interpretation of slope: Expected change in Sales by 7.681818182 when in area increases by one unit.
Interpretation of Intercept: The sales is  34.5 when area = 0.
d) The null and alternative hypothesis is
Level of significance = 0.01
Test statistic for slope is t = 6.82 ( Given in output)
Pvalue = 0.006453
Pvalue < 0.01 we reject null hypothesis.
Conclusion: There is a good contribution of an area in a model.
e) Coefficient of correlation = r = 0.9692 ( Given in output)
f) There is the strong correlation between sales and area.
g) Coefficient of determination = = 0.9394
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