Correlation and MR Theory Flashcards by Olivia Sterry

What are the three types of multiple regression

Simultaenous
Stepwise
Hierachical

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What are correlations and regressions used for

The study of the relationship between two or more variables and how they relate to each other

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When do yo do a regression opposed to a correlation

When there is more than one fixed variable

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What does regression allow

The prediction of Y on the basis of knowledge of X

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What does correlation allow

Measure of strength of relationship between X and Y

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How are correlations and multiple regressions plotted

Scatter plots

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What is a scatterplot

A 2-d diagram 1 point for each participant where coordinates are the scores

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What are correlation and scatter plots liked to

The degree to which the points cluster around the regression line

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What value does the regression and correlation lie between

-1 and +1

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What measure of association do you use when V1 and V2 are interval or ratio

Person’s

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What measure of association do you use with ordinal rank variables of ranking

Spearman’s rho

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What measure of association do you use when ordinal rank variables with opinions

Kendalls Tau

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What measure of association do you use with true dichotomy variables

Phi

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What measure of association do you use with a true dichotomy and interval variables

Point-Biseral

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How can a Venn diagram be used to represent a correlation

The size of the circles represents the variance of variable overlapping circles denote corrected variables

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What does a Venn diagram represent

Size of circles represents the variance of variable overlapping circles denote correlated variables

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What does a partial correlation look at

Measures the strength of dependence between 2 variables that is not accounted for by the a in which they both change in response to variations in a selected subset of other variables

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What is a multiple regression for

To learn about the relationship between several independent variables (predictors) and one dependent variable (criterion)

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What can multiple regressions create

Predictive tools

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What are examples of predictive tools

Estate agents analysing selling price for each house

Psychology studies on depression

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What is the general equation for multiple regressions

Ŷ = b0 + b1X1 + b2X2 + …. + bpXp

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What does the equation for linear regression involve

The linear equation finds the point on the Y axis it shifts and B gives the best predictive outcome of Y

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What is the objective of a multiple regression

Find the best fit with data

Minimize overall prediction error, hopefully to one predictor

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In the multiple regression equation what does the Y hat repreresent

predictive model of variable, tells what is the difference between the predictive score and what the actual score is. SS means sum of squares, subtract from predictive value then square it. Squaring gives more weight if near the line

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What does the MR equation give

The equation of a line b1 = slope | b0 = intercept

What does the equation assess

The goodness of fit based on similar things, and based on how far is the point from what is expected

In a multiple correlation coefficient if the correlation poor

Then poor model predictability

What is the symbol for the coefficient of determination

What is R2

Proportion of variability in data set accounted for by statistical model

What is the square of multiple correlation coefficient

F-ratio

What does the f ratio give in a multiple correlation coefficient

Improvement in prediction of criterion compared to inaccuracy of the model

What is the equation for assessing the goodness of the fit

R2 = SSM / SST or | F = MSM / MSR

What does the equation for assessing the goodness of the fit involve

Taking SS and dividing by DF

What does the equation of assessing the goodness of the fit punish for

Too many variables

What should be used instead of SS

What is the equation for MsM =

MSM = SSM / dfM MSR = SSR / dfR

What is the equation for number of variables in model

dfM

What is the number of observations equation

dfR (number of parameters being estimated)

What does a good model cause

A large improvement in prediction due to the model (Large MSm)

What does a small difference between model and data cause

A large F ratio, which can be used to measure how good the fit is in the data

What are the three ways to add terms to a model

Either put all the variables in, but more variables less generalised result

What are the 3 types of regression

Simultaneous Stepwise Hierarchical

What type of model does the simultaneous model have

No a priori model

How are all the IVs entered in a simultaneous regression

All IVs entered at once

What is a negative of the simultaneous regression

Over fitting the data

What type of model is a stepwise model

No a priori model

How are the IVs entered in a stepwise model

Computer choses, ons tats group, a posteriori model

What is a negative of a stepwise regression

Capitalises on chance effect

What is a strength of the hierarchical regression

Theoretically sound

How is the data entered in a hierarchical regression

A priori | driven by theory

What factors affect correlation

``` Outliers and inferential points Homo/heteroscedasciity Singularity and multi collinearity Number of cases vs number of predictors Range Distribution ```

What does homo/hetero-scedasticity- refer to

How well scattered the plots are

What does singularity and multi colineraity refer to

Independence of the variables, cant correlate .09

Define an outlier

Points which deviate markedly from other in sample

How is an outlier assessed

By cooks distance

Define homoscedasticity

Variability of scores (errors) in one continuous variable same in second variable – variable 1 to be similar to variable 2, uniform scatter across the line - uniform scatter

Define heteroscedasticity

One variable is skewed or the relationship is non-linear, tight variance then grows as X grows, X well distributed, and the more drastic this is the harder your model, your variance is homocentric.

Define singularity

Independent variables that don't relate in ant way

Define multi collineraity

Variables that are highly correlated >0.90

What is the problem of singularity

Dont want to measure the same thing twice, stats it prevents metric inversion

What are the solutions for singularity

High bivariate correlations >0.90 compute correlations and remove when appropriate

What is the solution for high multivariate correlations

Examine SMC (squared multiple correlation of each IV)

What is the tolerance level for high mutlivarate correlations

1 - SMC

Why is the number of cases important

N/M (number of cases / number of predictions) being too small will cause meaningless results

What is a medium effect size for multiple correlations

N > 50 + 8*m | m = number of predictors

What is a medium effect size for a simple linear regression

N > 104 + m – want N at least 100, more scores greater issue fitting them in a meaningful way

What is a medium effect size for a stepwise regression

N> 40* m | m = number of prediction

How can a small effect size or skewed DV or measurement error be measured

N > (8/f2) + (m – 1)

What figures indicates a small effect size with Cohens f2

0.02

What figure indicates a medium effect size with Cohens f2

0.15

What figure indicates a large effect size with Cohens f2

0.35

What is another issue with regressions

Range

Why is the range an issue with regressions

A small range restricts power of tests, want a good spread

What is the quartet relating to the distribution of variables

Anscombe's quartet

What is Anscombe's quartet

Same mean, variance, correlation and regression lin

What does Anscombe's quartet give

A strong effect without looking at the data

With 1+ IVs and aiming to predict IV from DV or relationship between what stats test do you use

Multiple regression

With 1+ IVs aiming to ask what is the relationship between 2 variables once effect of others removed what stats test do you use

Paritial correlation

When testing two sets of IV and trying to find what is common between the two what stats test do you use

Canonical correlation

How do you report a multiple regression

Table 3 displays the relationship between BART task performance and each predictor variable. Social risk taking (SOEPsoc): (b = .762) indicates that as BART score increases by one unit, social risk taking increases by .762. Social risking taking is the only significant predictor of BART task performance: t (492) = 4.345, p< .001. Indicating that social risk taking is the best predictor, out of the seven subscales, of BART task performance.