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
2133		369
3052		355.1
1074		181.5
1968		336.9
3062		614.2
2852		382.3
4292		655.7
2186		373.2
2496		407.4
1718		299.8
1718		260.1
3739		679

a) Which variable is the explanatory​ variable?

___Square Footage

___Selling Price

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

​(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.

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.

or a house that is 0 square​ feet, the predicted selling price is nothing thousand dollars.

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

B.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.)

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

increases by nothing thousand​ dollars, on average.

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

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

nothing.

​(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 not possible and 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.

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

C. Yeslong dash—a house of nothing square feet is possible and within the scope of the model.

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

D. Nolong dash—a

house of nothing square feet is 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 1409 square feet is sold for ​$270 thousand. Is this​ home's price above or below average for a home of this​ size?

The​ home's price is____the average price. The average price of a home that is

1409 square feet is ​$___thousand.

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

Answer 1

a)  Square Footage

b)

c) r= 0.907

d) No (because r=.907 implies high positive association but does not indicate a linear relation)

e) y = 16.0 + 0.16 x

f) option C is correct:

C. For every additional square​ foot, the selling price increases by 0.16 thousand​ dollars, on average.

g) Option A is correct

A. No—a house of 0 square feet is not possible and outside the scope of the model.

h) The​ home's price is below the average price. The average price of a home that is 1409 square feet is ​$241 thousand.

For any query, comment.