There is much more to logistic regression than I can cover in this short introduction,
but perhaps the biggest stumbling block that people experience is the movement to odds
and log odds when we are used to thinking about 0 and 1 or about probabilities. My major
purpose in this section was to get you past that barrier (and to supply you with arguments
why you should consider logistic regression over linear regression or discriminant analysis
when you have a dichotomous dependent variable). Everything else that could be said
about logistic regression is mainly about the technicalities, and you can find those in a
number of texts, particularly the ones by Allison (1999), Hosmer and Lemeshow (1989)
and Kleinbaum and Klein (2002).Exercises 571Key Terms
Regression coefficients (15.1)
Residual error (15.1)
Residuals (15.1)
Tolerance (15.2)
VIF (Variance Inflation Factor) (15.2)
Collinearity (15.2)
Multicollinearity (15.2)
Singular (15.2)
Importance (15.2)
Standardized regression
coefficients (15.2)
Residual variance (15.4)
Residual error (15.4)
Multivariate normal (15.5)
Multiple correlation coefficient
(R0.123.. .p)(15.6)
Hyperspace (15.7)
Regression surface (15.7)
Partial correlation (r0.12) (15.8)
Semipartial correlation (r0(1.2)) (15.8)
Venn diagrams (15.8)
Suppressor variable (15.9)
Multivariate outliers (15.10)
Distance (15.10)
Leverage (hi) (15.10)
Influence (15.10)
Cook’s D(15.10)
Studentized residual (15.10)
Nested models (15.10)
Hierarchical models (15.10)
Akaike’s Information
Criterion (AIC) (15.10)
All subsets regression (15.11)
Backward elimination (15.11)
Stepwise regression (15.14)
Forward selection (15.14)Cross-validation (15.14)
Listwise deletion (15.14)
Casewise deletion (15.14)
Pairwise deletion (15.14)
Imputing (15.14)
Mediating relationship (15.14)
Moderating relationships (15.14)
Center (15.14)
Logistic regression (15.15)
Discriminant analysis (15.15)
Conditional means (15.15)
Sigmoidal (15.15)
Censored data (15.15)
Logit (15.15)
Logit transformation (15.15)
Iteratively (15.15)Exercises
Note: Many of these exercises are based on a very small data set for reasons of economy of
space and computational convenience. For actual applications of multiple regression,
sample sizes should be appreciably larger than those used here.
15.1 A psychologist studying perceived “quality of life” in a large number of cities (N 5 150)
came up with the following equation using mean temperature (Temp), median income in
$1000 (Income), per capita expenditure on social services (Socser), and population density
(Popul) as predictors.a. Interpret the regression equation in terms of the coefficients.
b. Assume there is a city that has a mean temperature of 55 degrees, a median income of
$12,000, spends $500 per capita on social services, and has a population density of 200
people per block. What is its predicted quality of life score?3 YN =5.37 2 0.01 Temp 1 0.05 Income 1 0.003 Socser 2 0.01 Popul 4