# The Linear Model (L6) Flashcards

1
Q

Describe the equation for the linear model.

A

y = b0 + b1X1 + error

b1; parameter for the predictor, telling us the direction/strength of relationship (gradient)

b0; value of the outcome when predictor(s) = 0 (intercept)

2
Q

Describe what a graph with the same b0 but different b1 would look like.

A

Same intercept, different gradient.

3
Q

Describe what a graph with a different b0 but same b1 would look like.

A

Same gradient, different interept (lines run parallel to each other).

4
Q

What does it mean if the line of best fit is close to many data points?

A

The model is a good fit.

5
Q

What does it mean if the line of best fit is not close to many data points?

A

The model is a bad fit.

6
Q

What is the regression plane?

A

A 3-D line (square) that rotates around b0 depending on the value of b1.

7
Q

What is mulitple regression, and what is it’s equation?

A

y = b0 + b1X1 + b2X2 (…) + error

Same regression, but you add multiple predictors (X), each of which have a parameter (b).

8
Q

How does SPSS estimate parameter values, and where do you find them in the output?

A

Uses method of least squares; b1 is labelled as the parameter name, b0 is labelled as constant, both found in “B” column.

9
Q

What do significance tests do, in relation to b1 values?

A

Assess whether the predictor contributes to the model; ie., is the model significantly different from 0 (no effect).

10
Q

What do confidence intervals do, in relation to b1 values?

A

Assess the range of values b1 is likely to fall in, within the population.

11
Q

What are effect sizes?

A

Statistic which quantifies the relationship between variables.

12
Q

What are significance tests and CIs dependent on?

A

1) Sampling distribution normality
2) Homodescadicity.
3) Independe nt observations.

13
Q

When are parameter estimates optimal?

A

1) Residuals are normal

2) Homodescadicity

14
Q

What is bootstrapping?

A

The empirical estimation of CIs and variation of sample (SD). ‘An empirical guesstimate’. Used with small samples when you cannot assume normality.

15
Q

How is bootstrapping carried out?

A

1) A ‘bootstrap sample’ is calculated by randomly picking scores from data, which are then returned to the main sample so they could be chosen again. The bootstrap sample has the same number of data as original sample (eg. N=25 in both sample)
2) Mean estimated for bootstrap sample
3) Second bootstrap sample created, and mean estimated.
4) Steps 1-3 repeated 1000 times.

16
Q

What p-value do you use when bootstrapping?

A

SPSS produces a new ‘bootstrap output’ with a new p-value, therefore this value should be used when reporting your data.

17
Q

What is the total sum of squares (SST)?

A

Tells us the total variability of X from the mean. Calculated by adding up squared errors.

18
Q

What is the residual sum of squares (SSR)?

A

Tells us the residual/error variability and therefore the fit of the model in total and the error in the model.

19
Q

What is the model sum of squares (SSM)?

A

Tells us about the model variability, therefore if a model is better than no model (mean vs. model). Tells us through assessing the difference between data point and two lines (model and no model).

20
Q

How do you test the fit?

A

ANOVA or F-Test; compares the model to the error in the model using the average sum of squares;

F = MSm / MSr.

21
Q

What is R2 (R squared)?

A

Uses the sum of squares directly to express SSm as a portion of total variability (how much variability predictors account for)

R2 = SSm / SSt.

22
Q

What is adjusted R2?

A

The estimate of R2 in population (how the model generalizes to the world)

23
Q

What is shrinkage?

A

Difference between R2 and adj. R2;

R2 is smaller = sample isn’t representative.

24
Q

What is the predicted value?

A

The value from a solved equation.

25
Q

How do you calculate the t-statistic?

A

t = Bobserved / SEb.