Question

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.

Square​ Footage, x	Selling Price​ ($000s), y
21162116		366.2366.2
31243124		365.1365.1
11251125		189.4189.4
18771877		322.7322.7
31363136		624.2624.2
27382738		364.4364.4
42614261		650.7650.7
23062306		392392
27052705		440440
17801780		309.4309.4
18181818		275.8275.8
39463946		710.3

​(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?

Yes

No

​(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 the slope to three decimal places as needed. Round the intercept to one decimal place 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 sold for​ $0, the predicted square footage is .___

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

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

increase by ____ square​ feet, on average.

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

C. For a house that is 0 square​ feet, the predicted selling price is ____ thousand dollars.

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

D. For every additional square​ foot, the selling price increase by ___ thousand​ dollars, on average.

​(Round to three 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. Yes —a house of ____ square feet is possible and within the scope of the model.

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

B.No—a house of _____ square feet is outside the scope of the model

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

C.No —a house of ____ square feet is not possible.

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

D.No—a house of _______square feet is not possible and outside 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 14261426 square feet is sold for ​$265265 thousand. Is this​ home's price above or below average for a home of this​ size?

The​ home's price is the average price.(Options: 1.Below 2. Average The average price of a home that is 14261426 square feet is ___ thousand.

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

Answer 1

X: Square footage and Y: Selling price

c) Correlation coefficient (r)

Where n = 12 pairs of x and y

(d) The null and alternative hypotheses are:

H0: There is no linear relationship between the two variables

H1: There is a linear relationship between the two variables

r = 0.912

The critical value using the critical value table for correlation coefficient for degrees of freedom n - 2 = 10 and alpha for two tailed as 0.05 is 0.576

Critical value is less than r so reject the null hypothesis.

That is there is linear relation between square footage and asking price.

The answer is Yes

(e) Least square regression line

Where y - price

x - square footage

a - slope and b - intercept

The formula to find the slope

The formula of intercept

The least equare regression equation is

f) Interpretation of slope

It shows the increasde amount in x, if we increase x by 1 then y is increadsed by 0.158

Option D is correct

D. For every additional square​ foot, the selling price increase by 0.158 thousand​ dollars, on average.

g) Interpretation of intercept

If we take x as 0 then the price will increase by 9.7

But the house with 0 square footage is not possible, so option C is correct

C. No a house of 0 square feet is not possible.

h) x = 1426 and y = $265

Plug x = 1426 in the least square regression line to find yhat

The home price for 1426 square feet is $235

y - yhat = 265 - 235 = 30

The difference is positive so it is above average.