Choosing Regression Models

Question 1

SELECTING REGRESSORS

Answer 1

• potentially useful regressors have characteristics:
  1. to have “statsig effect” on DV
  2. able to discriminate between values of DV (categorical IV)
  3. to be strongly associated w/DV (continuous IV)

Question 2

CATEGORICAL VARIABLES: DV PREDICTION EVALUATION

Answer 2

• dichotomous variable (ie. gender)
• compare using t-test/ANOVA
• if statsig -> has discriminatory value
• can explain/predict variation in DV

Question 3

CONTINUOUS VARIABLES: DV PREDICTION EVALUATION

Answer 3

• continuous variable (ie. height)
• compare using correlation test
• if statsig -> discriminatory value
• can explain/predict variation in DV

Question 4

UNIVARIATE ANALYSES

Answer 4

• 1 IV
• one-way ANOVA
• simple linear regression

Question 5

MULTIVARIATE ANALYSES

Answer 5

• 1+ IV
• 2-way ANOVA
• multiple linear regression
• some regressor discriminatory value may be accounted for by regressors already present in model (ie. gender/income/height/age)
• adding regressor may not add as much to predictive value as anticipated
• impact of individual regressors can only be truly assessed “in presence of all other regressors”

Question 6

“IN THE PRESENCE OF ALL OTHER REGRESSORS”

Answer 6

• observed effect of any individual regressor in multiple regression model = only accurate:
  1. in presence of other specific regressors also in model
  2. for sample on which values are based
• if same regressor is entered into dif multiple regression model:
  1. coefficient values/direction likely to change
  2. statsig likely to change

Question 7

EFFECTIVENESS (VS EFFICIENCY)

Answer 7

• highest R^2 (most complete)
• will have more regressors
• will be effective BUT not efficient

Question 8

EFFICIENCY (VS EFFECTIVENESS)

Answer 8

• highest f-ratio (aka. Most statsig)
• will have single most important regressor
• will be efficient BUT not particularly effective

Question 9

EFFECTIVENESS VS EFFICIENCY: COMPROMISE

Answer 9

• will contain only “best” regressors available
• manageable number of regressors
• reasonably effective

Question 10

BEST MODEL FOR SAME REGRESSOR NUMBER

Answer 10

• Choose model w/highest R^2ADJ value
• Gives “best value” p/regressor
• Will also have acceptably high R^2/F-ratio value

Question 11

BEST MODEL FOR DIF REGRESSOR NUMBER

Answer 11

• Choose model w/2nd highest R^2ADJ value
• Best compromise between effectiveness/efficiency
• R^2 value reasonably high (effective; large % variance in DV explained)
• Reasonably high F-ratio value (efficient; only useful regressors included)