Karteikarten
Multiple Regression
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- 1Regression Formulay = b0 + b1x
- 2What is b0?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 - 3What is b1?b1 is the slope of the regression line
– It can be + or – - 4Is multiple regression the same as single regression?Yes, it just has more predictors.
Longer formula
• Each x is a different predictor with its own slope.
Note there is still only one DV (y) and only one intercept (b0) - 5How many IVs can there be?Theoretically, it's not limited.
the more data you have the mire independent vriables you can feasibly do. - 6What does e represent?The residuals, how far away the data points are from the line of best fit.
- 7R squaredThe amount y is because of x.
always use the adjusted r squared - 8Two predicters?3D graph,
each independent variables affects the dependt variable in its own way. - 9Outcome variableEssentially the dependent variable, affected by the predictor variables
- 10Predictor variablesThe variables which will affect the outcome variable
- 11Instead of a line of best fit?A plane of best fit, with two slopes
- 12Regression coefficientsUnstandardised
they relate to real units - 13Problem with regression coeficentswe cant compare different coefficents that used different units of measurements
- 14Standardised CoefficientsSPPS calls Beta
scales so they are always between -1 and +1
so different units can be compared - 15Coefficient of determinationR2 as a measure of explained variance.
Your stats package will produce R2
.
• This is quite simply the percentage of variation
in the DV which is explained by all the IVs
together in the regression model.
• There are two versions, non-adjusted and adjusted. SPSS always gives both. We just use adjusted because it’s better. - 16Interactions in multiple regressionits possible, similar to ANOVA
The relation between one IV and the DV is different depending on
the level of another IV.
• E.g. for some resilient students, the more I stress them, the more
they get done, whereas for less resilient students, stressing them
can be counterproductive - 17The statistical significance of a regression– Does the regression model explain more variance
than we expect by chance?
THere is a F value similar to ANOVA but we need to know the effect from each predidctor seprately for each predcitor there are there own p and t values - 18Different types of predictor entryEspecially with many predictors, researchers
often don’t just include them all in the model
right from the start.
• Entering them into the model all at once (like the previous example) is called the “entry”,
“simultaneous” or just “normal” method.
• Two other common methods are hierarchical and step-wise - 19Hierarchical regressionStarts by including some predictors, looks at model
properties, then adds some more predictors to see
what changes.
• A typical example would be if you are interested in the
extent to which, say, psychological trait A is predicted
by traits B and C, but you want to control for age and
gender.
• You start out with a model predicting A with just age
and gender, then in a new model include also B and C.
• R
2 will presumable have increased in model 2
compared to model 1. This change, known as ΔR
2 (delta r-squared) tells you how much variance in A is explained by B and C, while controlling for age and gender. - 20Step-wise regressionnot often used, as lots of reasons not too.
won't be in exam. - 21Standardised Beta ValuesStandardised values are easier to compare as they are not dependent
on the units of measurement of the variables
the predictors and outcome variables are mesured in terms of standard deviations - 22Coefficient (b) valueshow many outcomes variable will increase because of predictor variables, not standardised
- 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. - 24Linearity - assumptionsSame as simple regression
Linear regression.
This means a straight line.
Most easily checked visually: - 25Homoscedasticity• In ANOVA, the DV variation should be the same in the different groups (homogeneity of variance)
• In regression, similarly, the DV variation should be the same irrespective of the predictor value
• Also best checked
visually - 26heteroskedasticnot good
- 27MulticollinearityDoes not apply to simple regression
One new issue with multiple regression is that the different predictors should not be too strongly correlated.
• If two predictors were strongly correlated,
then how could the model separate their
contributions to predicting the outcome?
• Look at the correlation matrix for your
predictors. A rule of thumb is that you are OK as long as none are greater than .8 - 28—
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- U24137: Advanced Statistics and Experimental Method for Psychology Karteikarten am Multiple Regression, erstellt von Jasmine Stow am 12/11/2018.
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- Jasmine Stow
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