The Linear Model Flashcards
Why do we want to fit models?
To make predictions, everything we do is just a variation of a theme
How do we generalise our model?
We work on a small sample and develop our model from this - hoping it represents a large sample. for example, you wouldn’t just turn up and make a bridge, you have to plan it, making models (a small bridge) then see how it performs under different conditions = tells you how it would work in the real world
What are statistical tests?
Cases of the linear model - can do any test and end up with the same results
What is the equation of a straight line?
outcome = (b0+b1+x) + error
What does B1 represent?
Estimate of parameter for the predictor:
direction/strength of the relationship
difference in means
What does B0 represent?
Estimate of the value of the outcome when the predictor is 0 (intercept)
when everything is 0, what is the relationship between the predictor and outcome
What does X represent?
The predictors
What is the mean?
A very simple model, with one parameter and no predictors. its not a value actually observed, therefore there will be error
What does the mean give rise too?
The least deviations - least squared error
Why does the mean have the least squared error?
It is the score from which all of the scores will deviate the least from
estimating is based on minimising errors
How to estimate squared errors?
Difference between raw score and the mean
square these and add them up
What do most models use?
Ordinary least squares - minimises the error
What is it called when you extend the model?
Multiple regression
How do you enter predictors into the model?
Hierachal - best way - as the researcher, you make decisions about what goes first, good for theory testing, building on past knowledge rather than just guessing
Forced entry - all predictors are entered at the same time (ingredients in a cake)
Stepwise - predictors are selected using semi-partial correlation with the outcome. using what SPSS has found to have the biggest contribution, non-human, only for exploratory analyses, once one predictor is in, effects all of the others
What is the rate of change of B?
As something increases by one unit, how much does the outcome increase
Change in outcome associated with a change in predictor
What are standardised parameters?
Parameters which are expressed in standard deviations, means they are comparable because they are on the same scale
What does deviation refer too?
The observed value minus the predicted value
Why is adding up each persons error problematic?
Because the minuses and pluses will cancel each other out
Solution to adding up each persons error
Square each value
What is the sum of squared errors?
All of the errors in the data set
find the deviation
square each deviation
add all of these up
What is wrong with the sum of squared errors?
It is good, but it depends on how many scores there are in a data set. If different amount of scores, unfair as not a comparable measure
What do we use instead of sum of squared errors?
Mean squared error/variance
How do you calculate mean squared error/variance?
Sum of squares divided by degrees of freedom
What does the variance refer too?
The average error between the mean and observations made
What are degrees of freedom?
The amount of scores that are free to vary, to be any score they want
the last score in a data set has to be the one which aligns the score to the mean
What is SST?
Total variability between the scores and the mean
deviation squared added up
What is SSR?
The variability between the model and the data, the error in the model
What is SSM/regression?
Variability between the model and the mean
the improvement due to the model
If the model is better than the mean, what should we expect?
A bigger SSM compared to SSR
How to calculate F?
MSM divided by MSR - how good it is compared to how bad it is
What does R mean?
Correlation between predictors and outcome
What does R squared mean?
Variability accounted for by the model
SSM divided by SST
correlation between observed and predicted score
What does R squared adjusted mean?
An estimate of R square in the population
What does R square change mean?
How much model fit improves as more predictors are added
What is the F change?
How good it is compared to how good it isn’t
What does T mean?
Evaluates predictors, see which is useful
What does P mean?
Probability of getting a test statistic as big as one you have, if null hypothesis is true
