Midterm 2 - Chapt. 12 CONTINUED (From Nov 5th Lecture)

Question 1

REVIEW

What does r² represent?

Answer 1

Amount of SHARED VARIANCE in the DV that’s predictable from the IV

Example: A simple linear regression that predicts students’ exam scores (dependent variable) from their study time (independent variable) has an R² of . 71. From this R² value, we know that: 71% of the variance in students’ exam scores is predicted by their study time.

Question 2

What is Multiple Regression?

Answer 2

Extension of correlation
* Both measure relationships among variables
* Correlation does not imply causation

Question 3

What’s different about regression?

Answer 3

• Uses language of prediction
• Can use 1 or more variables to predict changes in another variable (still not causation!)

Question 4

How do regressions model predictive relationships

Answer 4

• Use score on one variable (“the Predictor”) to predict changes in another variable (“the Criterion”)
• Should use when we have a good reason that one of the variables could change the other (e.g., temporal precedence)

Question 5

When are regression/correlation methods used?

Answer 5

• Instead of experiments (typically)
• When you can’t manipulate variables, can only measure them
   E.g., ethical or practical problems
• Common in personality, health, & longitudinal/ developmental research

Question 6

What does b represent?

Y = a + bX

Answer 6

• Slope - Rise over Run

Question 7

What does a represent?

Y = a + bX

Answer 7

Intercept - when predictor (x) = 0, what’s the value of criterion (y)?

Question 8

What do Y and X represent?

Y = a + bX

Answer 8

• Y = criterion
• X = predictor

Question 9

Benefits of Regression Framework

Answer 9

Models predictive relationships
* When most appropriate - ie if you have temporal precedence, when you can’t use an experiment
Can investigate the effect of multiple predictors on the criterion at the same time.
* Ie Multiple Predictor Regression

Question 10

Multiple Regression Enables…

Answer 10

…investigation of how well many predictors simultaneously predict the criterion

• What’s the unique contribution of each predictor to the prediction of criterion?
• = what part of X1 overlaps with Y, which is UNIQUE and differentiates from the others

Question 11

Features of Multiple Correlation (R

Answer 11

• Can have any number of predictors
• Need to collect data on each predictor
• Calculate the unique contributions of each predictor individually on predicting criterion (b’s)
• Calculate the contribution of all predictors combined for predicting criterion
   Called the Multiple Correlation (R) but discussed as R 2
   R2 is the proportion of variance in the criterion that can
  be explained by all predictors combined

Question 12

Partial Correlation & the 3rd Variable Problem

Answer 12

• Statistically “control for” 3 rd variable
• Try to remove the effects of a variable we know likely influences both variables of interest
• EX: how much of the relationship between depression and anxiety is explained by anxiety? Once calculated, we can removed this aspect (the third variable)
• Correlation can decrease due to this removal - but STILL EXIST

Question 13

Measures of Relationship (R²)

Answer 13

• Correlation (r): Standardized index of how much two variables relate to each other
• Squared Correlation (r²): Proportion of variance shared by 2 variables
• Multiple Regression: A technique used when we want to test the unique contribution of one or more variables in predicting the criterion Y.
• Multiple Correlation (R/R²): A type of correlation coefficient that indexes how much a set of variables, when combined, is related to the criterion Y.
  - Used with multiple regression and expressed as R 2
• Partial Correlation: A correlation between X and Y that statistically removes the effect of Z

Question 14

What is the difference between multiple correlation and multiple regression?

Answer 14

Multiple Regression
* How much does each predictor uniquely contribute to explaining scores on the criterion?
* Calculation for each predictor separately

Multiple Correlation (R) – discussed as R2
* How much do all of the predictors combined explain scores on the criterion?
* One calculation for all of the predictors combined
* Can square R to identify the proportion of variance in the criterion that can be explained by all predictors combined.

Question 15

What is the difference between multiple correlation and partial correlation?

Answer 15

Multiple Correlation
 How much do all of the predictors combined explain
scores on the criterion?
 One calculation for all of the predictors combined

Partial Correlation
 How much is variable X related to variable Y, with the
effect of variable Z removed?
 How much is variable X related to variable Y,
controlling for the effect of variable Z?

Question 16

Advanced Modelling Techniques

Answer 16

• Structural Equation Modeling
• Measure 3 or more different variables
  ₋ What are the relationships amongst the variables?
  ₋ Model how multiple variables relate to (correlate
  with) each other and/or “predict” others.
  ₋ Should be some temporal precedence, but often
  data is cross-sectional

    E.g. Schooler & Mulatu, 2001
    – 1965, 1974, 1994
    - leisure cognitive activities & intellectual flexibility