Flashcards
Regression
Cards in this deck (27)
- 1Associationrelationships between two measured quantities that render them statistically independent.
Closely related to correlation.
Imply two or more variables co-vary - 2Co-varyTwo variables have a relationship.
e.g. one goes up so does the other - 3The line of best fitOr the trend line, is a straight line that best summarises the scatter plot data
- 4Correlation is represented by?p-value- chance value
r = how strongly the relationship is - 5Correlation vs RegressionCorrelation is just looking for how strong the correlation is between two numerical variable
Regression makes it possible to look at the relations between more than two numerical variables-multiple regression - 6Simple regressionjust one numerical IV predicting one numerical Dv but differs from corrleation as it tells you more than just one strenght of the association
- 7Correlation CoefficientThe relationship between two variables
If two variables co-vary, it means that knowing the
value of one gives you at least a clue about the value
of the other.
• The statistic typically used to measure co-variation
in two numeric (ratio or interval scale) variables is r.
• r is called the correlation coefficient
• More long-windedly called: the Pearson product moment
correlation coefficient, or just the Pearson
correlation coefficient
• r can between -1 and +1 - 8What does r show us?r summarises two important points:
1. Whether the slope of the scatterplot is positive or negative
2. The closeness of the fit of the points to the best-fitting straight line - 9Correlation & CausalityNo value of the correlation coefficient permits a researcher to
conclude that one variable influences the other
• As statisticians say: “Correlation does not imply causation”
• To prove that smoking causes cancer, a strong correlation was not
enough – they had to do an experiment where smoking was
manipulated (dogs were forced to smoke - 10The significance of and reporting rr has an associated p-value, representing the
chance of obtaining an r that extreme (far
from zero) if the null hypothesis is true.
• Report like this: “Pupil dilation and EEG
amplitude were correlated, Pearson’s r = .47,
p = .013, n = 29. - 11What does regression do?r tells you how closely two
variables co-vary, but it
doesn’t tell you how a change
in one predicts a change in
the other.
• Correlation is also not suitable for looking at
more complex relations between multiple
variables.
• We therefore need regression. - 12Linear regressionExamines the relations between one numerical
dependent variable and other numerical
independent variables
• Simple regression
– one independent variable (i.e. rather like correlation)
• Multiple regression
– as many independent variables as you like (within reason)
• (It’s actually possible to include categorical IV’s as
well, and it’s even quite easy with binary variables,
but this is beyond current scope.) - 13Simple (linear) regressionVariable X is the independent variable
– Also known as the predictor variable
• Variable Y is the dependent variable
– Also known as the criterion variable or outcome variable
• In order to describe the regression line, you need
– the slope (gradient) of the line
– the point at which it touches the vertical axis → the intercept
• Running the regression model tells you the value of these two
parameters - 14Making predictions - RegressionOne important use of regression is to establish a relation
between variables that can be used for purposes of prediction
• By establishing and describing this relation, regression provides
the basic information needed to make predictions
– using regression, we can predict the likely value of the DV, if we know the
value of the IV
• Remember, correlation does not equal causation
– although knowing about violent TV watching allows us to make a decent
educated guess (prediction) about aggression, that doesn’t mean violent
TV causes aggression
• However, for some purely correlational designs, we can make
conclusions about causation based on logic
– E.g., if age and life satisfaction correlate, direction of causation is clear! - 15How to do Simple regression?For maths GCSE, you probably learnt how to describe a straight line
on a graph as:
y = mx + c
• For regression, we normally say (but it’s the same):
y = b0 + b1
x
• b0 is the intercept, the point at which the regression cuts the vertical
axis at X = 0
– It can take + or – value, denoting whether the vertical axis is cut above or below
its zero point
– What’s the value here?
• b1 is the slope of the regression line
– It can be + or –
– What’s the value here? - 16What is the letter for regression coefficient?b
- 17What is the formula?y=b0+b1x
b0 is the intercept
b1 is the slope of the data - 18Dealing with uncertainty - regressionRecall that all parameters calculatedfrom
samples are estimates of the true population values.
• We don’t actually care about the exact values from the sample except insofar as they give us clues about the population.
– That’s why there is little value in e.g. the mean of a small sample
• We want an idea of how close our sample estimates are to the population values.
• This applies not just to means, but also to things like regression coefficients (b0
and b1) - 19Confidence Intervals95% sure that the population mean is between x and x
the bigger the sample the more confident we are. - 20Standardised coefficientsRegression coefficients as we’ve dealt with them are unstandardized – they relate to real units.
• For our example, b1 = 9.5 means that for every 1mm change in pupil dilation, we get a 9.5 µV change in EEG amplitude.
• The only problem with this is we can’t compare different regression coefficients that used different units (e.g. does parental income or education best predict children’s school grades).
• Standardised coefficients (what SPSS calls beta) are scaled so that they are always between -1 and 1 (like r).
• This will make more sense in the context of multiple regression. - 21The statistical significance of a regressionThe most common way to assess whether a regression model is significant is actually just like ANOVA:
– Does the regression model explain more variance than we expect by chance?
• So there is actually an ANOVA-style F-ratio associated with the model, along with a pvalue.
• For our example, F(1,25) = 7.17, p = .013. - 22R2 as a measure of explained variance (coefficient of determination)• This is quite simply the percentage of variation in the DV which is explained by the IVs (based on the regression model).
can do on SPSS - 23Linear regression: three main assumptions which need to holdLinearity
– The outcome variable should be linearly related to any predictors.
• Normally distributed residuals (not raw data)
• Homoscedasticity
– The residuals at each level of the predictor should have the same variance.
– Remember homogeneity of variance for ANOVA? It’s just like that. - 24LinearityLinear regression.
• This means a straight line.
• Most easily checked visually: - 25HomoscedasticityIn ANOVA, the DV variation should be the same in the difference groups (homogeneity of variance)
• In regression, similarly, the DV variation should be the same irrespective of the predictor value
• Also best checked
visually
Heteroscedastcicty - the bigger the x gets the more variance there is in the data - 26Heteroscedasticitythe bigger the x gets the more variance there is in the data
Not good! - 27—
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- U24137: Advanced Statistics and Experimental Method for Psychology Flashcards on Regression, created by Jasmine Stow on 05/11/2018.
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