Final session 12a

Question 1

Linear regression assumes that:

Answer 1

We have independent observations
linearity
Values of Y are independent
Variance of errors does not depend on the value of the predictor, X1
Errors, or residuals in the population, are normal

Question 2

explain linearity

Answer 2

Relationship between predictor and outcome is linear in the population

Question 3

explain Values of Y are independent

Answer 3

and random sampling & random assignment are used

Question 4

explain Variance of errors does not depend on the value of the predictor, X1

Answer 4

The variance of Y at every value of X1 is the same Homogeneity of variance, or homoscedasticity

Question 5

explain Errors, or residuals in the population, are normal

Answer 5

Y is normally distributed at each value of X1 (normality)

Question 6

what is normality

Answer 6

Y is normally distributed at each value of X (normality)

Errors, or residuals in the population, are normal

Question 7

explain Homogeneity of Variance Assumption

Answer 7

The variance of Y at every value of X is the same

Question 8

how to go about Checking Assumptions:

Answer 8

Graphical Analysis of Residuals - “Residual Plot”

Question 9

Plot residuals (e) vs. Yˆi do what

Answer 9

Examine functional form (Linear vs. Nonlinear)
One predictor at a time: e vs. Xi values also possible

Evaluate homoscedasticity

Question 10

Multiple regression means what

Answer 10

we have more than one predictor variable, or IV

Question 11

for Multiple” Regression, we describe how the DV (Y ) changes as what change

Answer 11

multiple IVs (Xj )

Question 12

Questions leading to use of multiple regression:

Answer 12

Can we improve prediction of Y with more than one IV? Does our experiment have more than one IV?
Does our theory say that more than one IV affects the DV?

Question 13

Equation for regression line:

Answer 13

Yˆ = b 0 + b 1 X 1 + b 2 X 2 + · · · b J X J

Question 14

explain Intercept (b0)

Answer 14

Expected (average) value of Y when all predictors are equal to zero

Question 15

explain Slopes (e.g., bj)

Answer 15

Expected change in Y when Xj increases by 1 unit, holding all other
predictors constant

Effect of Xj on Y , controlling for other predictors1
If we equate observations on the other predictors, what effect does Xj have?

Unique predictive effect of Xj on Y above and beyond other predictors Similar to a partial correlation

Question 16

Testing individual regression coefficients, hypotheses

Answer 16

H0 :βj =0
Xj has no (unique) linear relationship with Y

H1 :βj doesn’t equal 0
A t-test can again be used

Question 17

Proportion of total variance in Y accounted by what

Answer 17

the regression model

Can be estimated by:
R2 = SSM / SST

Question 18

what are the factors of Squared multiple correlation (R2)

Answer 18

Ranges from 0 to 1

Larger R2, more variance of DV explained 0: No explanation; 1: Perfect explanation

Question 19

If new IV is added to the model, how does R2 change?

Answer 19

SSM will increase, and SSR will decrease
R2 will always increase
Even if the new IV is not related to the DV in the population
This increase may not be significantly different than zero

Question 20

what is Adjusted R2

Answer 20

Provides unbiased estimate of proportion of variance explained in the population

If a new IV is added that doesn’t help predict the outcome, Adjusted R2 may decrease