Excel add-in option that is available from the Excel installation CD. After
installation, it is listed in yourToolsmenu. The process is rather simple: Click
(1) theTools, then (2)Data Analysis. Among the functions available, choose
REGRESSION. A box appears; use the cursor to fill in the ranges ofYand
X’s. The results include all items mentioned in this chapter, plus confidence
intervals for regression coe‰cients.
EXERCISES
8.1 Trace metals in drinking water a¤ect the flavor of the water, and un-
usually high concentration can pose a health hazard. Table E8.1 shows
trace-metal concentrations (zinc, in mg/L) for both surface water and
bottom water at six di¤erent river locations. Our aim is to see if sur-
face water concentration (x) is predictive of bottom water concentration
(y).TABLE E8.1
Location Bottom Surface
1 0.430 0.415
2 0.266 0.238
3 0.567 0.390
4 0.531 0.410
5 0.707 0.605
6 0.716 0.609(a)Draw a scatter diagram to show a possible association between the
concentrations and check to see if a linear model is justified.
(b)Estimate the regression parameters, the bottom water concentration
for location with a surface water concentration of 0.5 mg/L, and
draw the regression line on the same graph with the scatter diagram.
(c)Test to see if the two concentrations are independent; state your
hypotheses and choice of test size.
(d)Calculate the coe‰cient of determination and provide your inter-
pretation.
8.2 In a study of saliva cotinine, seven subjects, all of whom had abstained
from smoking for a week, were asked to smoke a single cigarette. The
cotinine levels at 12 and 24 hours after smoking are provided in Table
E8.2.
(a)Draw a scatter diagram to show a possible association between the
cotinine levels (24-hour measurement as the dependent variable) and
check to see if a linear model is justified.306 CORRELATION AND REGRESSION