Fundamentals of Probability and Statistics for Engineers

(b) Estimate

11.11 In Problem 11.7, when vehicle weight is taken into account, we have the multiple
linear regression equation

where w is vehicle unladen weight in Mg. Use the data given in Table 11.11 and

estimate the regression parameters in this case.

11.12 G iven the data in Table 11.12:

(a) D etermine the least-square estimates of 0 , 1 ,and 2 assuming that

(b) Estimate

11.13 A large number of socioeconomic variables are important to account for mortal-
ity rate. Assuming a multiple linear regression model, one version of the model for
mortality rate (Y) is expressed by

where

x 1 mean annual precipitation in inches,

x 2 education in terms of median school years completed for those over 25 years

old

x 3 percentage of area population that is nonwhite,

x 4 relative pollution potential of SO 2 (sulfur dioxide).

Table 11.10 Data for Problem 11.10

x 1 1 1112233

x 2 1 2345678

y 2.0 3.1 4.8 4.9 5.4 6.8 6.9 7.5

Table 11.11 N oise level, y (in dB), with vehicle weight (unladen,

in Mg) and vehicle speed (in km h^1 ), for Problem 11.11

v 20406080100120

w 1.0 1.0 1.7 3.0 1.0 0.7

y54597891 78 67

Table 11.12 Data for Problem 11.12

x 01234567

y 3.2 2.8 5.1 7.3 7.6 5.9 4.1 1.8

362 Fundamentals of Probability and Statistics for Engineers

EfYgatx 1 ˆx 2 ˆ2.

Yˆ 0 ‡ 1 log 10 v‡ 2 log 10 w‡E;

EfYgˆ 0 ‡ 1 x‡ 2 x^2 :

EfYgatxˆ3.

Yˆ 0 ‡ 1 x 1 ‡ 2 x 2 ‡ 3 x 3 ‡ 4 x 4 ‡E;

ˆ

ˆ

ˆ

ˆ