4. Model Fit and multiple predictors

Question 1

b1 is an estimate of…

Answer 1

parameter for a predictor
-> direction\strength of relationship/effect
-> difference in means

Question 2

b0 is an estimate of…

Answer 2

the value of the outcome when predictor(s) = 0 (intercept)

Question 3

What do sums of squares represent?

Answer 3

Total error

Question 4

Because sums of squares are totals, we can compare them only when…
Alternatively, we factor in…

Answer 4

When they are based on the same number of scores
the number of scores

Question 5

When comparing sums of squares, we can get the average error by…

Answer 5

divide by a function of the number of scores

Question 6

What is meant by the illusory truth effect (ITE)?

Answer 6

Repetition increases perceived truthfulness.
This is equally true for plausible and implausible statements

Question 7

Each total sum of squared errors (SS(T)) has associated what?

Answer 7

Degrees of freedom (df)

Question 8

What is degrees of freedom?

Answer 8

The amount of independent information available to compute SS

Question 9

For each parameter (p) estimated we lose…?

Answer 9

1 piece of independent information

Question 10

How do we get the residual sum of squared errors (SS(R))?

Answer 10

To begin with we have N pieces of independent information.
To get SS(R) we estimate two parameters (b0 and b1).

Question 11

The model sum of squared errors (SS(M)) is a rotation of the null model. What one piece of info are the null model and the estimated model distinguished by?

Answer 11

The slope (b1)
(Note, the intercept, b0, co-depends on the
slope - it is not an independent piece of information)

Question 12

A sum/total of squared errors depends on…

Answer 12

The amount of information used to compute it

Question 13

The average or mean squared error can be computed by…

Answer 13

Dividing the SS by the amount of information used to compute it

Question 14

What is the Mean Squared error R?

Answer 14

• Average residual/error variability (variability between the model and the observed data) - How badly the model fits (on average)

Question 15

What is the mean squared error M?

Answer 15

• Average model variability (difference in variability between the model and the grand mean)
• How much better the model is at predicting Y than the mean
• How well the model fits (on average)

Question 16

If the model results in better prediction than using the mean, then ____ should be greater than ____

Answer 16

MS(M) should be greater than MS(R)

Question 17

What is the F statistic?

Answer 17

The ratio of MS(M) to MS(R) (the good to shit ratio)

Question 18

What is R^2?

Answer 18

The proportion of variance accounted for by the model
The Pearson correlation coef cient between observed and predicted scores squared

Question 19

What is adjusted R^2?

Answer 19

An estimate of R2 in the population (shrinkage)

Question 20

What do the following three ways of entering predictors mean?
1. Hierarchical
2. Forced entry
3. Stepwise

Answer 20

1. Experimenter decides the order in which variables are entered into the model
   Best for theory testing
2. All predictors are entered simultaneously
3. Predictors are selected using their semi-partial correlation with the outcome
   Can produce spurious results
   Use only for exploratory analysis

Question 21

We evaluate fit of a general linear model using…?

Answer 21

Sums of Squared Errors (SS)

Question 22

What do the following stand for?
1. SS(T)
2. SS(R)
3. SS(M)

Answer 22

1. SST = the total variance/error in observed scores
2. SSR = the total variance/error in predicted scores
3. SSM = the total reduction in variance/error due to the model

Question 23

What do the following mean squared errors (MS) mean?
1. MS(R)
2. MS(M)

Answer 23

1. MSR = the average variance/error in predicted scores
2. MSM = the average reduction in variance/error due to the model

Question 24

What is ‘F’?

Answer 24

the average variance accounted for by the model compared to the model’s error in prediction

Question 25

bs are the change in the outcome associated with a unit change in the predictor when…

Answer 25

when others predictors are held constant (in red so important lol)