Applied Statistics and Probability for Engineers

394 CHAPTER 11 SIMPLE LINEAR REGRESSION AND CORRELATION

which simplifies to

Minitab will also calculate prediction intervals. Refer to the output in Table 11-2. The 95% PI

on the future observation at x 0 1.00 is shown in the display.

By repeating the foregoing calculations at different levels of x 0 , we may obtain the 95%

prediction intervals shown graphically as the lower and upper lines about the fitted regression

model in Fig. 11-8. Notice that this graph also shows the 95% confidence limits on

calculated in Example 11-5. It illustrates that the prediction limits are always wider than the

confidence limits.

Y 0 x 0

86.83y 0 91.63

Figure 11-8 Scatter

diagram of oxygen

purity data from

Example 11-1 with

fitted regression line,

95% prediction limits

(outer lines) and 95%

confidence limits on

Y 0 x 0.

90

87

93

96

99

102

0.87 1.07 1.27 1.47 1.67

Hydrocarbon level (%)

x

Oxygen purity

y (%)

EXERCISES FOR SECTIONS 11-6 AND 11-7

11-31. Refer to the data in Exercise 11-1 on yintrinsic

permeability of concrete and xcompressive strength. Find

a 95% confidence interval on each of the following:

(a) Slope (b) Intercept

(c) Mean permeability when x2.5

(d) Find a 95% prediction interval on permeability when

x2.5. Explain why this interval is wider than the

interval in part (c).

11-32. Exercise 11-2 presented data on roadway surface

temperature xand pavement deflection y. Find a 99% confi-

dence interval on each of the following:

(a) Slope (b) Intercept

(c) Mean deflection when temperature

(d) Find a 99% prediction interval on pavement deflection

when the temperature is.

11-33. Exercise 11-4 presented data on the number of

games won by NFL teams in 1976. Find a 95% confidence in-

terval on each of the following:

90 F

x 85 F

(a) Slope (b) Intercept

(c) Mean number of games won when opponents rushing

yardage is limited to x 1800

(d) Find a 95% prediction interval on the number of games

won when opponents rushing yards is 1800.

11-34. Refer to the data on yhouse selling price and

xtaxes paid in Exercise 11-5. Find a 95% confidence inter-

val on each of the following:

(a) 1 (b) 0

(c) Mean selling price when the taxes paid are x7.50

(d) Compute the 95% prediction interval for selling price

when the taxes paid are x7.50.

11-35. Exercise 11-6 presented data on ysteam usage

and xmonthly average temperature.

(a) Find a 99% confidence interval for  1.

(b) Find a 99% confidence interval for  0.

(c) Find a 95% confidence interval on mean steam usage

when the average temperature is 55 F.

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