Introduction to Probability and Statistics for Engineers and Scientists

414 Chapter 9: Regression

2. The following data relate the number of units of a good that were ordered as a
   function of the price of the good at six different locations.

Number ordered 88 112 123 136 158 172

Price 50 40 35 30 20 15

How many units do you think would be ordered if the price were 25?

3. The corrosion of a certain metallic substance has been studied in dry oxygen at
   500 degrees Centigrade. In this experiment, the gain in weight after various periods
   of exposure was used as a measure of the amount of oxygen that had reacted with
   the sample. Here are the data:

Hours Percent Gain

1.0 .02

2.0 .03

2.5 .035

3.0 .042

3.5 .05

4.0 .054

(a) Plot a scatter diagram.

(b) Fit a linear relation.

(c) Predict the percent weight gain when the metal is exposed for 3.2 hours.

4. The following data indicate the relationship betweenx, the specific gravity of
   a wood sample, andY, its maximum crushing strength in compression parallel to
   the grain.

xi yi(psi) xi yi(psi)

.41 1,850 .39 1,760

.46 2,620 .41 2,500

.44 2,340 .44 2,750

.47 2,690 .43 2,730

.42 2,160 .44 3,120

(a) Plot a scatter diagram. Does a linear relationship seem reasonable?

(b) Estimate the regression coefficients.

(c) Predict the maximum crushing strength of a wood sample whose specific

gravity is .43.