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 Selling Price ($000s), y

2095 362.9

3122 364.9

1085 183.2

1935 331.9

3149 626.8

2772 370.3

3963 604.3

2170 370.5

2710 440.8

1695 296

1763 267.5

3723 675.7

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

o Square Footage

0 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= ___

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

​(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.

(h) One home that is 1493 square feet is sold for ​$225 thousand. Is this​ home's price above or below average for a home of this​ size?

Answer 1

a) Explanatory variable is the independent variable . Here square footage is the explanatory variable.

b) The scatter plot is as shown below. Ignore the trend line in the plot.

750 700 650 600 550 500 450 400 350 300 250 200 150 100 500 1000 1500 2000 2500 3000 3500 4000 4500

c)The linear correlation coefficient r=0.9002d) The linear regression line is y= 12.51+0.157x

Step 1: Find X-Y, X2 and Y2 as it was done in the table below X.Y 760275.5 1139217.8 198772 642226.5 1973793.2 1026471.6 2394840.9 803985 1194568 501720 471602.5 2515631.1 y.Y 131696.41 133152.01 33562.24 110157.61 392878.24 137122.09 365178.49 137270.25 194304.64 87616 71556.25 456570.49 2095 3122 1085 1935 3149 2772 3963 2170 2710 1695 1763 3723 362.9 364.9 183.2 331.9 626.8 370.3 604.3 370.5 440.8 296 267.5 675.7 4389025 9746884 1177225 3744225 9916201 7683984 15705369 4708900 7344100 2873025 3108169 13860729 Step 2: Find the sum of every column to get ΣΧ = 30182, ΣΥ= 4894.8, ΣΧ.Y= 13623104.1, ΣΧ2= 84257836, ΣΥ2-225106472 Step 3: Use the following formula to work out the correlation coefficient. 12 13623104.1- 30182 4894.8 0.9002 νΊ12-84257836-301822] . [12-225106472-4894.81

where y is the selling price and x is the square footage.

Step 1: Find X .Y and X2 as it was done in the table below 4389025 9746884 1177225 3744225 9916201 7683984 15705369 4708900 7344100 2873025 3108169 13860729 2095 3122 1085 1935 3149 2772 3963 2170 2710 1695 1763 3723 362.9 364.9 183.2 331.9 626.8 370.3 604.3 370.5 440.8 296 267.5 675.7 760275.5 1139217.8 198772 642226.5 1973793.2 1026471.6 2394840.9 803985 1194568 501720 471602.5 25156311 Step 2: Find the sum of every column ΣΧ= 30182, Σ , Σ , ΣΧ-84257836 Y = 4894.8 X Y 13623104.1 Step 3: Use the following equations to find a and b Σ Υ . ΣΧ. ΣΧ . Σ ΧΥ 4894.8-84257836-30182 . 136231041 12-84257836 301822 -n . Σ ΧΥ-Σ x . Σ Υ = 12-13623104:1-30 182-48948 0 157 12-84257836-(30182)2 Step 4: Substitute a and b in regression equation formula y = 12.51 + 0.157-

f) For every additional square​ foot, the selling price increases by 0.157 thousand​ dollars, on average.

option B is correct.

g) It is not reasonable to interpret the y intercept. Because y-intercept is the selling price of the home whose square foot is 0 which is not possible in real life.

h)for x=1493 the predicted y value is y= 12.51+(0.157*1493) = $246.911 thousand

given home that is 1493 square feet is sold for $225 thousand which is below the average for a home of this size.

For any query please comment below.