what is the difference between correlation and regression?
correlation is about explaining a relationship, whereas regression is about predicting values based on a fixed variable
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what 3 ways can we characterise a relationship (correlation)?
strength, form, direction
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what does monotone mean?
movement in one direction
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what does non-parametric mean?
among other things it does not assume a line, unlike parametric statistics?
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is Kendall's tau parametric or non-parametric?
non-parametric
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which is sensitive to outliers, Pearson's r or Kendall's tau?
Pearson's r
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what steps are involved in comparing independent correlations?
compute the 2 correlations, transform each using Fisher's z, divide the difference by standard error
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what are 4 properties of good residuals?
no systematic trends, equally variable (homoscidacity), normally distributed, no outliers
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what does R squared show? what does an R squared of 0.65 say?
an overall index of fit; the model accounts for 65% of variance in the data.
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when would you use multiple regression?
when you have more than one predictor
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what does collinearity mean?
this is when predictors are highly correlated, producing a naturally stronger relationship
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what are some symptoms of collinearity?
CC changes radically when new predictors are added, large standard error, the R squared does not increase with each addition, high VIF, strong predictors are insignificant.
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what would you use if you wanted to predict a response variable using many predictors?
multiple regression
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what would you use if you want to determine how much benefit a single predictor gives?
part/semi-partial correlation
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what would you use if you want to examine the strength of a relationship while holding other variables constant?
partial correlation
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would option do you have when the intercept is not meaningful/useful/in possible range?
centring
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if we want to use discrete predictors, what would we have to do first?
dummy coding
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what do you have to do to variables before putting them into an interaction?
centre them
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do you centre continuous variables and discrete variables in the same way?
no, subtract the mean for continuous, subtract the half-way point for discrete,
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what is the guideline value that indicates VIF is problematic?
9
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what does an interaction in correlation/regression mean?
the slope of a variable is different depending on the value of another variable.
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does linear regression need a linear relationship to work?
no
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what does polynomial regression do?
allows the slope to change with x
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does more parameters always mean a better prediction?
no, a perfect fit often means a terrible prediction of new samples
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what is a statistical method for dealing with overfitting?
look at the adjusted R squared, and whether it is significantly smaller than original r squared.
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what are two non-statistical ways of dealing with over-fitting?
replication and cross-validation
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how does cross validation work?
split data into parts, fit a curve to one part, test fit of curve in the other part
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what 3 ways can we characterise a relationship (correlation)?
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