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Chapter 12 Multiple Linear Regression and Certain Nonlinear Regression Models

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x

y

Estimatc thc quadratic regression cquation p_Y\x = 3o + 0\X+ 02X².

12.8 The Ibllowing is a set ofeoded cxpcrimcntal data on thc comprcssivc strength of a particular alloy at var-ious valucs of thc conccnlration of somc additivc:

Concentration,    Compressive

X    Strength, >■

10.0	25.2	27.3	28.7
15.0	29.8	31.1	27.8
20.0	31.2	32.6	29.7
25.0	31.7	30.1	32.3
30.0	29.4	30.8	32.8

(a)    Estimatc thc quadratic regression cquation p.y\_x = 00 + 0lX+ 02X².

(b)    Test for lack of fit of thc model.

12.9 The clcctric power consumcd cach month by a Chemical plant is thought to be related to thc avcragc ambient temperaturę xi, thc number of days in thc month X2.^lhc avcragc product purity 13, and the tons of product produccd xą. The past ycar's historical data arc available and arc presented in thc following table.

V	21	X2	®3
240	25	24	91	100
236	31	21	90	95
290	45	24	88	110
274	60	25	87	88
301	65	25	91	94
316	72	26	94	99
300	80	25	87	97
296	84	25	86	96
267	75	24	88	110
276	60	25	91	105
288	50	25	90	100
261	38	23	89	98

(a)    Fil a multiple linear regression model using thc abovc data set.

(b)    Prediet power consumption for a month in which Xi = 75°F, X2 = 24 days, 13 = 90%, and x.i = 98 tons.

12.10 Givcn thc data

4 5    6

2 3    4

(a) Fit the cubic model py\x = &o + /?ix-P#2*²/?3X³.

(b) Prediet Y when x = 2.

scorcs of four tests. The data arc as follows:

_ y	XI	X2		24
11.2	56.5	71.0	38.5	43.0
14.5	59.5	72.5	38.2	44.8
17.2	69.2	76.0	42.5	49.0
17.8	74.5	79.5	43.4	56.3
19.3	81.2	84.0	47.5	60.2
24.5	88.0	86.2	47.4	62.0
21.2	78.2	80.5	44.5	58.1
16.9	69.0	72.0	41.8	48.1
14.8	58.1	68.0	42.1	46.0
20.0	80.5	85.0	48.1	60.3
13.2	58.3	71.0	37.5	47.1
22.5	84.0	87.2	51.0	65.2

Estimatc thc regression cocfficicnts in thc model y = bo + biXi+ 62X2+ 63X3+ 64X4.

12.12 The following data rcflcct information taken from 17 U.S. Naval hospitals at various sites around thc world. The regressors arc workload variables, that is, items that result in thc need for pcrsonncl in a hos-pital installation. A brief dcscription of thc variablcs is as follows:

y = monthly labor-hours,

X\ = avcragc da i 1 y paticnl load.

X2 = monthly X-ray cxposurcs,

X3 = monthly occupicd bed-days,

x,j = cligiblc population in the arca/1000.

X5= avcragc lcnglh of paticnt's stay. in days.

Sitc	*1	X2	x3	Xą	®5	V
1	15.57	2463	472.92	18.0	4.45	566.52
2	44.02	2048	1339.75	9.5	6.92	696.82
3	20.42	3940	620.25	12.8	4.28	1033.15
4	18.74	6505	568.33	36.7	3.90	1003.62
5	49.20	5723	1497.60	35.7	5.50	1611.37
6	44.92	11520	1365.83	24.0	4.60	1613.27
7	55.48	5779	1687.00	43.3	5.62	1854.17
8	59.28	5969	1639.92	46.7	5.15	2160.55
9	94.39	8461	2872.33	78.7	6.18	2305.58
10	128.02	20106	3655.08	180.5	6.15	3503.93
11	96.00	13313	2912.00	60.9	5.88	3571.59
12	131.42	10771	3921.00	103.7	4.88	3741.40
13	127.21	15543	3865.67	126.8	5.50	4026.52
14	252.90	36194	7684.10	157.7	7.00	10343.81
15	409.20	34703	12446.33	169.4	10.75	11732.17
16	463.70	39204	14098.40	331.4	7.05	15414.94
17	510.22	86533	15524.00	371.6	6.35	18854.45

12.11 The pcrsonncl deparlmenl of a certain indus- The goal herc is to producc an cmpirical cquation that trial firm uscd 12 subjccts in a study to dcterminc thc will estimatc (or prediet) pcrsonncl nccds for Naval relationship bctwccn job performance rating (y) and hospitals. Estimatc thc multiple linear regression cqua-