Question

$3,198,000
$1,450,000
$5,375,000
$3,648,000
$5,195,000
$5,345,000
$5,495,000
$16,300,000
$7,395,000
$9,995,000
$13,500,000
$11,995,000
$5,245,000
$6,350,000
$7,199,000
$5,498,000
$23,000,000
$6,890,000
$37,500,000
$16,950,000
$13,995,000
$7,400,000
$10,900,000
$33,400,000
$18,500,000
$18,995,000
$10,995,000
$11,995,000
$10,995,000
$23,995,000
$2,648,000
$18,900,000
$39,995,000
$9,500,000
$29,000,000

2,089 sqft

1,961 sqft

4,415 sqft

2,083 sqft

5,352 sqft

3,458 sqft

2,763 sqft

11,438 sqft

4,847 sqft

5,007 sqft

5,639 sqft

6,306 sqft

2,892 sqf

2,626 sqft

4,346 sqft

1,814 sqft

9,000 sqft

6,195 sqft

16,450 sqft

5,269 sqft

5,047 sqft

4,173 sqft

5,134 sqft

17,000 sqft

11,872 sqft

6,424 sqft

7,451 sqft

6,244 sqft

6,495 sqft

9,200 sqft

2,204 sqft

5,880 sqft

15,328 sqft

1,518 sqft

11,491 sqft

Using the data collected, find the relationship between any two quantitative variables

a) Perform a correlation analysis

b) Perform a regression analysis .Develop a linear regression mathematical model that would help make a prediction based on a given dependent variable.

c) Discuss the findings of your regression analysis. Interpret slope, coefficient of determination in context on problem

d) Provide the scatter plot. (20)

Answer 1

Excel > Data > Data Analysis > Regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.913814181
R Square	0.835056357
Adjusted R Square	0.830058065
Standard Error	4085011.67
Observations	35
ANOVA
	df	SS	MS	F	Significance F
Regression	1	2.78792E+15	2.78792E+15	167.0683352	1.82875E-14
Residual	33	5.50682E+14	1.66873E+13
Total	34	3.3386E+15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-620067.5902	1266733.768	-0.489501114	0.627725157	-3197256.819	1957121.639	-3197256.819	1957121.639
SQFT(X)	2189.673105	169.4073354	12.92549168	1.82875E-14	1845.01129	2534.33492	1845.01129	2534.33492

a)

Correlation coefficient (r) = 0.9138

Hypothesis:

H0​:ρ=0

HA​:ρ̸​=0

Test:

t stat = r*SQRT((n-2)/(1-r^2)) = 0.9138*SQRT((35-2)/(1-0.9138^2)) = 12.924

P value = 0

P value < 0.05, reject H0

There is enough evidence to conclude that there is a significant linear relationship between x and y varaibles

b)

Hypothesis:

H0: β1 = 0

Ha: β1 not = 0

Test:

F stat = 167.07

P value = 0

P value < 0.05, reject H0

Therefore regression model is statistically significant

Regression equation:

Y = -620067.5902+2189.6731*X

c)

Slope interpretation:

If sqft increases by 1 unit, price increases by 2189.6731 units

Coefficient of determination (r^2) = 0.8351

83.51% of variation in price is explained by variation in sqft or regression model

d)