3. Exercise 4.3

The county assessor is studying housing demand and is interested in developing a regression model to estimate the market value (i.e., selling price) of residential property within her jurisdiction. The assessor suspects that the most important variable affecting selling price (measured in thousands of dollars) is the size of house (measured in hundreds of square feet). She randomly selects 15 houses and measures both the selling price and size, as shown in the following table.

Complete the table and then use it to determine the estimated regression line.

Observation	Size	Selling Price
	(x 100 sq. ft.)	(x $1,000)
ii	xixi	yiyi	xixi yiyi	xi2xi2	yi2yi2
1	12	265.2	3,182.40	144.00	70,331.04
2	20.2	279.6	5,647.92	408.04	78,176.16
3	27	311.2	8,402.40	729.00	96,845.44
4	30	328.0	9,840.00	900.00	107,584.00
5	30	350.0	10,500.00	900.00	122,500.00
6	21.4	281.2	6,017.68	457.96	79,073.44
7	21.6	284.4	6,143.04	466.56	80,883.36
8	25.2	292.8	7,378.56	635.04	85,731.84
9	37.2	356.0	13,243.20	1,383.84	126,736.00
10	14.4	263.2	3,790.08	207.36	69,274.24
11	15	272.4	4,086.00	225.00	74,201.76
12	22.4	291.2	6,522.88	501.76	84,797.44
13	23.9	299.6	7,160.44	571.21	89,760.16
14	26.6	307.6	8,182.16	707.56	94,617.76
15	30.7	320.4	9,836.28	942.49	102,656.16
Total	357.60	4,502.80	selector 1 101,750.88 91,914.60 109,933.04	9,179.82	selector 2 1,363,168.80 1,076,134.72 994,980.16

Points:

Regression Parameters	Estimations
Slope ( )	selector 1 3.95 -0.64 60.64
Intercept ( )	selector 2 315.44 -1,145.47 206.00

Points:

Close Explanation

Explanation:

In words, for each hundred square feet, the expected selling price of a house selector 1

• decreases
• increases

by $ selector 2

• 60,640
• 640
• 3,950

.

Points:

Close Explanation

Explanation:

What is the standard error of the estimate (sese )?

9.886

9.843

9.510

Points:

Close Explanation

Explanation:

What is the estimate of the standard deviation of the estimated slope (sbsb )?

0.386

0.372

0.385

Points:

Close Explanation

Explanation:

Can the assessor reject the hypothesis (at the 0.05 level of significance) that there is no relationship (i.e., =0=0 ) between the price and size variables? (Hint: t0.025,13=2.160t0.025,13=2.160 )

Yes

No

Points:

Close Explanation

Explanation:

Complete the following worksheet and then use it to calculate the coefficient of determination.

ii	xixi	yiyi	yy^	(yiy)2y^iy2	(yiy)2yiy^2	(yiy)2yiy2
1	12	265.2	253.4	2,189.0	139.2	1,224.1
2	20.2	279.6	285.8	207.0	38.4	423.8
3	27	311.2	312.7	156.6	2.3	121.3
4	30	328.0	324.5	591.1	12.3	773.6
5	30	350.0	324.5	591.1	650.3	2,481.4
6	21.4	281.2	290.5	93.8	86.5	360.5
7	21.6	284.4	291.3	79.0	47.6	249.2
8	25.2	292.8	305.5	28.2	161.3	54.6
9	37.2	356.0	352.9	2,778.7	9.6	3,115.1
10	14.4	263.2	262.9	1,390.3	0.1	1,368.0
11	15	272.4	265.3	1,217.1	50.4	772.1
12	22.4	291.2	294.5	32.3	10.9	80.8
13	23.9	299.6	300.4	0.0	0.6	0.3
14	26.6	307.6	311.1	119.1	12.3	55.0
15	30.7	320.4	327.3	735.1	47.6	408.6
			Total	selector 1 11,598.7 10,208.4 9,326.0	selector 2 1,957.0 1,269.4 986.3	selector 3 11,059.3 11,009.6 11,488.4

Points:

The coefficient of determination (r2r2 ) is selector 1

• 0.923
• 1.010
• 0.889

Points:

Close Explanation

Explanation:

The F-ratio is selector 1

• 0.110
• 8.042
• 104.545

, which means that the assessor selector 2

• can
• cannot

reject, at the 5% level of significance, the null hypothesis that there is no relationship between the selling price and the area of the house. (Hint: The critical value of F0.05,1,13F0.05,1,13 is 4.67.)

Points:

Close Explanation

Explanation:

Which of the following is an approximate 95% prediction interval for the selling price of a house having an area (size) of 15 (hundred) square feet?

177.4 to 215.4

245.5 to 285.1

176.6 to 216.2