5. Regression Flashcards
What is correlation?
Standardised covariance between two variables.
Why is the least squares solution so named?
It attempts to minimise the residual SS - so least squares.
What are degrees of freedom for residual?
Total sample size, minus number of predictors, minus 1
What are degrees of freedom for regression?
Number of predictors.
If more predictors added to equation, what happens to R square?
It gets bigger.
What can happen to the bs if IVs are highly intercorrelated?
R square might be significant, but none of the bs will be.
Why is b called the partial regression coefficient?
Because b represents the expected change in DV (units) while controlling for other IVs.
When should b, the unstandardised regression coefficient, be used?
- When variables are in a meaningful metric
- To explore policy implications
- To compare results across samples or studies
When should β, the standardised regression coefficient, be used?
- When variables are not in meaningful metric
2. To compare relative effects of different IVs in the same study.
When is missing data considered a concern?
Usually only when it’s over 5%
When can sizes of b be used to compare relative importance of predictors in same sample?
When they are in the same metric, e.g. hours or centimetres.
Should common causes be included in regression model?
Hell yeah! They must be included in order to interpret regression coefficients as effects validly.
Do mediating variables have to be included to interpret regression coefficients as effects?
No. They’re just variables lying in between the cause and the effect – there could be any number of them, really, but they don’t reduce causality.
Is a high R square more important for explanation or prediction?
For prediction.
If you want to make statements about the effects of one variable on another, your interest is ____________
If you want to make statements about the effects of one variable on another, your interest is EXPLANATION.
E.g., Conservatism predicts life satisfaction. But doesn’t explain it. Conservatives more likely to be married, religious, etc. –these variables also account for some of the variance in life satisfaction
What kind of effect does simultaneous regression estimate?
Direct effects.
Regression weights in simultaneous regression change depending on ____________________
Regression weights in simultaneous regression change depending on the variables entered.
In sequential regression, tests of the bs are affected by ____________.
In sequential regression, tests of the bs are effected by order of entry.
What does a test of b reflect in sequential regression?
A test of b reflects the proportion of variance, say, VarX1 accounts for in VarY when it is entered in the analysis last. I.e. over and above the variables entered before it.
What test statistic does t square for the b coefficient correspond to in sequential regression?
The F statistic for the test of delta R square (R square change)
Sequential MR estimates the variance due to __________ effects
Sequential MR estimates the variance due to total effects. 18/10
Does the order of entry in sequential regression change the overall R square?
No, but the order of entry will affect what portion of variance is explained by each variable.
What is the formula for semipartial (part) correlation?
Square root of delta R square.
What is the semipartial (part) correlation?
The correlation of Y with X1, when the effects of X2, X3 etc. are removed from X1 (not DV). So the effect over and above all other effects.
How can you determine the unique effect/variance of a variable?
Square the semipartial (part) correlation.
What’s the long way of getting semipartial (part) correlations?
Do several sequential regressions, entering each variable last.
How do you calculate the total variance in the DV explained by a variable?
By squaring the zero-order correlation with the DV..
How do you calculate the unique variance in the DV explained by a variable?
By squaring the PART correlation with the DV.
How do you calculate the shared variance between variables?
By taking R square and subtracting the unique variance of each variable from it.
In simple bivariate regression, r is equal to what regression coefficient?
Beta, the standardised regression coefficient
In simple bivariate regression, from which other values can R square be derived?
By squaring r or Beta.
