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 his 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). He 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	xixiyiyi	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	109,933.04	9,179.82	1,363,168.80

Regression Parameters	Estimations
Slope (ββ)	3.95
Intercept (αα)	206.00

In words, for each hundred square feet, the expected selling price of a house by $ .

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

9.843

9.886

9.510

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

0.372

0.385

0.386

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

Yes

No

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

ii	xixi	yiyi	yˆy^	(yˆi−y¯)2y^i−y¯2	(yi−yˆ)2yi−y^2	(yi−y¯)2yi−y¯2
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

The coefficient of determination (r2r2) is

The F-ratio is , which means that the assessor 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.)

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

176.6 to 216.2

245.5 to 285.1

Answer rating: 100% (QA)

Solution The estimated regression line is Selling price 20600 395 size The standard erro... View the full answer