Question

The biggest determining the value of a home square footage accompanying data represent the square footage and selling price for a random sample of homes for sale in a certain region

Sample Footage, x. Selling Price ($000s), y

2292. 393.8

3216 381.5

1074 181.5

1948 333.8

3196 634

2670 354

4126 629.7

2126 363.8

2637 429.4

1707 298.1

1855 281.9

3930 708.6

a.) determine the linear correlation coefficient between square footage and asking price

b.) find the least squares regression line treating square footage as the explanatory variable

c.) interpret the slope

for every additional square foot, the selling price increased by ______ thousand dollars, on average

d.) is it reasonable to interprey the y-intercept? why?

a house of ___ square feet is not possible and outsidw the scope of the model

e.) one home that is 1431 square feet is sold for $210 thousand. is this home’s price above or below average for a homr of this size?

the average price of a home that id 1431 feet id $______ thosand.

Answer 1

X	Y	XY	X²	Y²
2292	393.8	902589.6	5253264	155078.44
3216	381.5	1226904	10342656	145542.25
1074	181.5	194931	1153476	32942.25
1948	333.8	650242.4	3794704	111422.44
3196	634	2026264	10214416	401956
2670	354	945180	7128900	125316
4126	629.7	2598142.2	17023876	396522.09
2126	363.8	773438.8	4519876	132350.44
2637	429.4	1132327.8	6953769	184384.36
1707	298.1	508856.7	2913849	88863.61
1855	281.9	522924.5	3441025	79467.61
3930	708.6	2784798	15444900	502113.96
Ʃx =	Ʃy =	Ʃxy =	Ʃx² =	Ʃy² =
30777	4990.1	14266599	88184711	2355959.45

Sample size, n =	12
x̅ = Ʃx/n = 30777/12 =	2564.75
y̅ = Ʃy/n = 4990.1/12 =	415.841667
SSxx = Ʃx² - (Ʃx)²/n = 88184711 - (30777)²/12 =	9249400.25
SSyy = Ʃy² - (Ʃy)²/n = 2355959.45 - (4990.1)²/12 =	280867.949
SSxy = Ʃxy - (Ʃx)(Ʃy)/n = 14266599 - (30777)(4990.1)/12 =	1468240.03

a) Correlation coefficient, r = SSxy/√(SSxx*SSyy)

= 1468240.025/√(9249400.25*280867.94917) = 0.9109

b) Slope, b = SSxy/SSxx = 1468240.025/9249400.25 = 0.158738944

y-intercept, a = y̅ -b* x̅ = 415.84167 - (0.15874)*2564.75 = 8.715960963

Regression equation :   

ŷ = 8.716 + (0.1587) x  

c) For every additional square foot, the selling price increased by 0.1587 thousand dollars, on average

d) No, it is not reasonable to interpret the y-intercept.

A house of 0 square feet is not possible and outside the scope of the model.

e) Predicted value of y at x = 1431

ŷ = 8.716 + (0.1587) * 1431 = $ 235.87

The average price of a home that is 1431 feet is $235.87 thousand.

This home’s price is below average for a home of this size.