# The Linear Model (L6) Flashcards

Describe the equation for the linear model.

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)

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

Same intercept, different gradient.

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

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

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

The model is a good fit.

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

The model is a bad fit.

What is the regression plane?

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

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

y = b0 + b1X1 + b2X2 (…) + error

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

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

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

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

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

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

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

What are effect sizes?

Statistic which quantifies the relationship between variables.

What are significance tests and CIs dependent on?

1) Sampling distribution normality

2) Homodescadicity.

3) Independe nt observations.

When are parameter estimates optimal?

1) Residuals are normal

2) Homodescadicity

What is bootstrapping?

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

How is bootstrapping carried out?

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.