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.

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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)...

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5.25.2
5.35.3
5.45.4
5.55.5
5.75.7
5.75.7
5.85.8
6.16.1
6.26.2
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