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
2138   369.6
3278   389.4
1168   196.1
1973   337.8
3185   633
2860   384.9
4046   617.3
2130   364.4
2492   406.7
1679   293.4
1826   277.1
3820   691.5

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

Selling Price

Square Footage

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

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

r=__?__

​(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.

ŷ =__?__ x+l(__?__)

​(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 sold for​ $0, the predicted square footage is __?__.

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

B.

For every additional square​ foot, the selling price increases by __?__thousand​ dollars, on average.

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

C.

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

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

D.

For every additional thousand dollars in selling​ price, the square footage increases by __?__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.

No—a house of __?__square feet is outside the scope of the model

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

B.

No—a house of __?__square feet is not possible.

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

C.

No — a house of __?__square feet is not possible and outside the scope of the model.

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

D.

Yes—a house of __?__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 1468square feet is sold for $280 thousand. Is this​ home's price above or below average for a home of this​ size?

The​ home's price is

▼

below

above

the average price. The average price of a home that is 1468 square feet is

​$__?__thousand.

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

Answer 1

(a) The explanatory​ variable=Square Footage

(b)

(c)

Pearson correlation of Square Footage and Selling Price ($000s)=r = 0.902

(d) Yes, there is a linear relation between square footage and asking​ price.

(e)

(f) Option: B. For every additional square​ foot, the selling price increases by 0.16 thousand​ dollars, on average.

(g) Option C. No Selling price of a house of 0 square feet is not possible and outside the scope of the model.

(h) If x=1468 then predicted selling price=18.13+0.16*1468= 253.01 thousand​ dollars

So the home's price is above the average price. The average price of a home that is 1468 square feet is 253 thousand​ dollars.