Applied Statistics and Probability for Engineers

378 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION

and

Therefore, the least squares estimates of the slope and intercept are

and

The fitted simple linear regression model (with the coefficients reported to three decimal places) is

This model is plotted in Fig. 11-4, along with the sample data.

Computer software programs are widely used in regression modeling. These programs

typically carry more decimal places in the calculations. Table 11-2 shows a portion of the out-

put from Minitab for this problem. The estimates and are highlighted. In subsequent sec-

tions we will provide explanations for the information provided in this computer output.

Using the regression model of Example 11-1, we would predict oxygen purity of 

89.23% when the hydrocarbon level is x1.00%. The purity 89.23% may be interpreted as

yˆ

ˆ 0 ˆ 1

yˆ74.28314.947 x

ˆ 0 yˆ 1 x92.1605 1 14.94748 2 1.19674.28331

ˆ 1 

Sx y

Sx x



10.17744

0.68088

14.94748

Sx y a

20

i 1

xiyi

aa

20

i 1

xib aa

20

i 1

yib

20

2,214.6566

1 23.92 21 1,843.21 2

20

10.17744

Sx xa

20

i 1

x (^) i^2 
aa
20
i 1
xib
2
20
29.2892
1 23.92 22
20
0.68088
90
87
93
96
99
102
0.87 1.07 1.27 1.47 1.67
Hydrocarbon level (%)
Oxygen purity
y (%)
x
Figure 11-4 Scatter
plot of oxygen
purity yversus
hydrocarbon level x
and regression model
yˆ74.2014.97x.
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