Final session 13a

Question 1

what are the main parts of Multiple linear regression

Answer 1

Continuous independent variables

Categorical independent variables
-Dummy coding

Question 2

what are the Type of linear regression for Analysis of covariance (ANCOVA)

Answer 2

Categorical and continuous IVs at the same time

No interaction between categorical and continuous IVs

Question 3

what are the Motivations for ANCOVA

Answer 3

In experiments, subjects are randomly assigned to experimental conditions

• We expect that subjects will be roughly equal on background variables
• But, random assignment does not explicitly control for background variables

If random assignment is not used, different experimental conditions may not be well matched on background variables
-If groups are not well-matched, such extraneous variables may be confounding variables

Extraneous variables (including possible confounders) may also help predict the DV

• If we have good theory, we can measure these variables
• We can include such variables as covariates, or predictors in our model

Question 4

what are Confounding variable

Answer 4

In correlational designs, confounding variables are the classic “third variable” that may explain who the IV and DV are related

If random assignment fails to equate groups on the confounding variable or random assignment is not used, this may also explain group differences

Question 5

(ANCOVA) Including covariates can result in two things:

Answer 5

1 Reduction in mean squares residual

2 Elimination of confounds

Question 6

Analysis of covariance (ANCOVA) does what

Answer 6

controls for (or removes) the influence of extraneous variable on the DV

Question 7

The extraneous variable is called what

Answer 7

the covariate in ANCOVA

Question 8

How does ANCOVA work?

Answer 8

1 Influence of covariate is removed from the DV using linear regression
2 Remaining effect of the categorical IV is applied to residuals
i.e., portion of the DV left unexplained by the covariate
The tests of difference across the means of residuals is similar to ANOVA Means of residuals are called adjusted means

Question 9

ANCOVA and adjusted means:

The effect of the categorical IV is a joint test of b1 and b2 H0 :β1 =β2 =0
Conceptually, this is what

Answer 9

like running on ANOVA on adjusted means

Question 10

How to obtain adjusted means

Answer 10

Means of the groups, adjusting for the covariate
In other words, at the mean value of the covariate (Z bar)

We can obtain these from our regression line by substituting appropriate values
Yˆ = b 0 + b 1 X 1 + b 2 X 2 + b 3 Z

Question 11

Partitioning variation in ANCOVA: Total variation, SST , is partitioned into:

Answer 11

SSM : Variation in Y explained by the regression model SSR: Variation in Y unexplained by the regression model

Question 12

But, SSM, or the model includes variation explained by: (in ANCOVA)

Answer 12

The categorical IV
The covariate
Portion where both the categorical IV and covariate overlap

This means that SSM can be further partitioned
We obtain tests for the unique effects of both the categorical IV and the covariate