Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 8 Regression and Correlation 345

a relationship anywhere near as strong as the relationship between mortal-

ity index and temperature that you worked with earlier in the chapter.

Save your work and close the Calculus Correlation Analysis workbook.

Exercises

1. True or false, and why: If the slope of a
   regression line is large, the correlation
   between the variables will also be large.


2. True or false, and why: If the correla-
   tion between two variables is near 1, the
   slope will be a large positive number.


3. True or false, and why: If the p value of
   the Pearson’s correlation coeffi cient is
   low, the p value of the slope parameter of
   the regression equation will also be low.


4. True or false, and why: A correlation of
   zero means that the two variables are
   unrelated.
   5. True or false, and why: The runs test is
   one of the diagnostic tests you should
   always apply to the residuals in your
   regression analysis.
   6. In a time-ordered study, you have 25
   residuals from the regression model.
   There are 10 negative residuals and
   15 positive ones. There are a total of
   10 runs. Is this an unusual number of
   runs? What is the level of statistical
   signifi cance?
   7. Using the following ANOVA table for
   the regression of variable y on variable x,
   answer the questions below.

Table 8-6 Regression of Variable y on x

ANOVA df SS MS F Signifi cance F
Regression 1 129.6 129.6 4.91 0.057
Residual 8 210.9 26.4
Total 9 340.5

a. How many observations are in the

data set?

b. What is the variance of y?

c. What is the value of R^2?

d. What percentage of the variability in y

is explained by the regression?

e. What is the absolute value of the cor-

relation of x and y?

f. What is the p value of the correlation

of x and y?

g. What is the standard error (the typical

deviation of an observed point from

the regression line)?

8. Return to the Breast Cancer Mortality
   study discussed in this chapter. There
   may be an outlier in the data set.
   Perform the following analysis to
   determine the effect of this outlier on
   the regression analysis:
   a. Open the Breast Cancer workbook
   from the Chapter08 folder and save it
   as Breast Cancer Outlier Regression
   to the same folder.
   b. Remove the observation for the fi rst
   region from the data set.