122 CHAPTER 7 Correlation, Regression, and Logistic Regression
7.7 EXERCISES
- D e fi ne the following terms:
(a) Association
(b) The Pearson correlation coeffi cient
(c) Simple linear regression
(d) Multiple linear regression
(e) Nonlinear regression
(f) Scatter plot
(g) Slope of the regression line in simple linear regression - What assumptions are needed for the Pearson correlation coeffi cient to be
a meaningful measure of the relationship between two variables? - What is the mathematical relationship between the correlation coeffi cient
and the slope of the simple linear regression line? Can the slope be nega-
tive and the correlation be positive? If the correlation is zero, what is the
value of the slope? - Regarding outliers:
(a) How would you defi ne an outlier?
(b) Does an outlier always imply an error in the data?
(c) Give an example of an outlier that represented an error in the data.
(d) Give an example where the outlier is more important to the research
than the other observations. - What is logistic regression? How is it different from ordinary linear
regression? - How does multiple linear regression differ from simple linear
regression? - What is the defi nition of the multiple correlation coeffi cient R 2?
- How is R 2 useful in evaluating the goodness of a model?
- What is the equivalent to R 2 in simple linear regression?
- What is multicollinearity? Why does it pose problems estimating regres-
sion parameters? - What is stepwise regression? Why is it used?
- Refer to Table 7.5. A psychiatric epidemiologist studied information he
collected on the anxiety and depression levels for 11 subjects. Produce a
scatter diagram for anxiety score on the x - axis and depression score on
the y - axis.