# TB6/7 RM Topic Overview

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- Created by: mint75
- Created on: 17-11-15 15:42

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- RM TB6/7 Overview
- Linear Regression
- A way of predicting outcomes you have not measured
- Creates a linear model of the relationship between two variables
- What to look for
- R(squared)= The % of variance accounted for by the model
- SSM (SST/SSR)= The amount of improvement by using the 'best' model over the 'dumb' model
- The F Ratio = The ratio of the MSM (regression) error to the mean square residual error. A larger F = smaller p value

- y = b1x + b0

- Correlation
- A way of measuring the extent to which two variables are related
- DOES NOT IMPLY CAUSATION
- What to look for
- Correlation Coefficient (r) = Divide the covariance by the product of the individual STDDES
- Should always be between -1 and +1, 0 = no relationship.
- A standardised measure of the size AND direction of the relationship

- Covariance = Sum of the cross-product deviations, divided by n - 1
- Tells you the DIRECTION but not size of the relationship

- Correlation Coefficient (r) = Divide the covariance by the product of the individual STDDES
- Non-parametric alternatives
- Spearmans Rho (assumptions violated)
- Kendalls Tau (small data set with tied ranks)

- Partial correlations
- Used to control for other potential mediating variables, the EXCLUSIVE relationship of x to y

- Multiple Regression
- The multiple regression equation
- y = b0 + b1x1 + b2x2 +...bnxn + residuals (eta)

- Different methods of regression
- Managing the order of variables you're fitting
- Forced Entry
- Hierarchical
- Stepwise

- Managing the order of variables you're fitting
- Interpreting multiple regression
- R2 - The proportion of variance accounted for by the model
- Adjusted R2 = An estimate of R2 in the population (shrinkage)
- You want these to be similar, meaning the model could generalise to the population

- Adjusted R2 = An estimate of R2 in the population (shrinkage)
- ANOVA F Statistic; Tells us whether the regression model is a better predictor than the mean (dumb) model
- Beta Values
- The change in the outcome associted with a unit change in the predictor
- Standardised beta values = the same but as STDDEV
- The change in the outcome associted with a unit change in the predictor

- R2 - The proportion of variance accounted for by the model
- Predicts the values of an outcome variable from several predictors
- How well does the model fit the data?
- Residual statistics (Standardised residuals)
- Confidence intervals, 1.96+-

- Influential cases (Cooks distance)
- Measures the influence of a single case on the whole model, values > 1 = bad

- Residual statistics (Standardised residuals)

- The multiple regression equation
- Standardised Beta Values
- A beta value tells us the CHANGE in the outcome variable associated with unit change in predictor
- The standardised betas tell us the same but expressed as a STDDEV
- e.g B1 = 0.523, as adverts increased by 1 STDDEV, sales increased by 0.523 of a STDDEV
- These allow us to directly compare the effects of variables

- e.g b1 = 0.087, as adverts incresed by £100 sales increased by 0.087 units

- The standardised betas tell us the same but expressed as a STDDEV
- Factor Analysis
- Tests for 'clusters' of variables. Which measures are ASPECTS of a common dimension? How many are there?
- Use correlation (R) matrix
- Aiming to reduce the R-matrix into SMALL sets of UN-CORRELATED dimensions

- Use Factor matrix to assess factor loadings
- How much does each question contribute to each factor?

- Principal Component Analysis (PCA) = finds the principal axis of a cloud of data points, allowing you to find factors (FA)
- Use Eigenvectors, reduce multidimensional data sets into a set of components
- Eigenvalues tell you how important each eigenvector is
- Scree Plots
- Look for the point of inflexion, as opposed to Kaiser extraction where you only use eigenvalues > 1

- Rotation
- Maximises the loading of a variable on one factor whilst minimising load on all other factors
- Orthoganol (VARIMAX) both axes are rotated to go through the center of the clouds, factors are UNCORRELATED

- Use Eigenvectors, reduce multidimensional data sets into a set of components
- Reliability
- Test-retest method and Split half method
- Cronbachs alpha, data is reliable if a > 0.7
- Although affected by number of items
- Reverse score reverse phrased items!

- A beta value tells us the CHANGE in the outcome variable associated with unit change in predictor
- Also note assumptions of each test

- Linear Regression

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