Question

Square Footage, x   Selling Price ($000s), y
2241   385.8
3197   376.3
1099   185.4
1979   338.6
3044   611.2
2725   363.7
3930   599.1
2131   364.4
2703   439.7
1691   295.6
1847   280.5
3985   716.6

One of the biggest factors in determining the value of a home is the square footage. The accompanying data represent the square footage and selling price​ (in thousands of​ dollars) for a random sample of homes for sale in a certain region. Complete parts​ (a) through​ (h) below.

LOADING...

Click the icon to view the housing data.

​(a) Which variable is the explanatory​ variable?

Selling Price

Square Footage

​(b) Draw a scatter diagram of the data. Choose the correct scatter diagram below.

A.

10004000150750xy

A scatter diagram has a horizontal axis from 1000 to 4000 in increments of 500 and a vertical axis from 150 to 750 in increments of 50. A series of plotted points loosely forms a line that rises from left to right and passes through the points (1100, 190) and (3990, 720).

B.

15075010004000yx

A scatter diagram has a horizontal axis from 150 to 750 in increments of 50 and a vertical axis from 1000 to 4000 in increments of 500. A series of plotted points loosely forms a line that rises from left to right and passes through the points (190, 1100) and (720, 3990).

C.

10004000150750xy

A scatter diagram has a horizontal axis from 1000 to 4000 in increments of 500 and a vertical axis from 1000 to 4000 in increments of 50. A series of plotted points loosely forms a line that falls from left to right.

D.

10004000xy

A scatter diagram has a horizontal axis from 1000 to 4000 in increments of 500 and a vertical axis from 1000 to 4000 in increments of 500.A series of plotted points strictly forms a line that rises from left to right and passes through the points (1000, 1000) and (4000, 4000).

​(c) Determine the linear correlation coefficient between square footage and asking price.

requals=nothing

​(Round to three decimal places as​ needed.)

​(d) Is there a linear relation between square footage and asking​ price?

No

Yes

​(e) Find the​ least-squares regression line treating square footage as the explanatory variable.

ModifyingAbove y with caretyequals=nothingxplus+left parenthesis nothing right parenthesis

​(Round to two decimal places as​ needed.)

​(f) Interpret the slope. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.For a house that is 0 square​ feet, the predicted selling price is

nothing

thousand dollars.

​(Round to two decimal places as​ needed.)

B.For a house that is sold for​ $0, the predicted square footage is

nothing.

​(Round to two decimal places as​ needed.)

C.For every additional square​ foot, the selling price

increasesincreases

by

nothing

thousand​ dollars, on average.

​(Round to two decimal places as​ needed.)

D.For every additional thousand dollars in selling​ price, the square footage

increases

by

nothing

square​ feet, on average.

​(Round to two decimal places as​ needed.)

E.

It is not appropriate to interpret the slope.

​(g) Is it reasonable to interpret the​ y-intercept? Why? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

Nolong dash—a

house of

nothing

square feet is outside the scope of the model

​(Type an integer or a simplified​ fraction.)

B.

Nolong dash—a

house of

nothing

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

​(Type an integer or a simplified​ fraction.)

C.

Nolong dash—a

house of

nothing

square feet is not possible.

​(Type an integer or a simplified​ fraction.)

D.

Yeslong dash—a

house of

nothing

square feet is possible and within the scope of the model.

​(Type an integer or a simplified​ fraction.)

E.

More information about the houses is necessary before deciding.

​(h) One home that is

1450

square feet is sold for

​$216

thousand. Is this​ home's price above or below average for a home of this​ size?The​ home's price is

▼

above

below

the average price. The average price of a home that is

1450

square feet is

thousand.

​(Round to the nearest whole number as​ needed.)

Click to select your answer(s).

Answer 1

using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9030
R Square	0.8155
Adjusted R Square	0.7970
Standard Error	69.5802
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	213943.4704	213943.4704	44.1903	0.0001
Residual	10	48414.0721	4841.4072
Total	11	262357.5425
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	11.5901	63.6481	0.1821	0.8591	-130.2267	153.4069
x	0.1576	0.0237	6.6476	0.0001	0.1048	0.2104

a)
explanatory variable is independent variable ( x) = square footage

b)

c)
r = 0.815

d)
p-value = 0.0001 < alpha
hence
yes

e)
y^ = 11.59 + 0.16 *x

f)
slope
option C)
For every additional square​ foot, the selling price increases by 0.16

g)
No
It is not possible to have area = 0

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