My regression lecture mk3 (uploaded to web ct)Presentation Transcript
SIMPLE AND MULTIPLE REGRESSION Chris Stiff [email_address]
In this lecture you will learn:
What simple and multiple regression mean.
The rationale behind these forms of analyses
How to conduct a simple bivariate and multiple regression analyses using SPSS
How to interpret the results of a regression analysis
What is regression?
Regression is similar to correlation in the sense that both assess the relationship between two variables
Regression is used to predict values of an outcome variable (y) from one or more predictor variables (x)
Predictors must either be continuous or categorical with ONLY two categories
Simple regression involves a single predictor variable and an outcome variable
Examines changes in an outcome variable from a predictor variable
Outcome = dependent, endogenous or criterion variable.
Predictor = independent, exogenous or explanatory variable.
The relationship between two variables can be expressed mathematically by the slope of line of best fit.
Usually expressed as
Y = a + b X
Outcome Intercept + (Coefficient x Predictor)
Y = Outcome (e.g., amount of stupid behaviour)
a = Intercept/constant (average amount of stupid behaviour is nothing is drunk
b = Unit increment in the outcome that is explained by a unit increase in the predictor – line gradient
X = Predictor (e.g., amount of alcohol drunk)
LINE OF BEST FIT Amount of alcohol Stupid behaviour
LINE OF BEST FIT – POOR EXAMPLE Stupid behaviour Number of pairs of socks ?
SIMPLE REGRESSION USING SPSS
Analyze Regression Linear
SPSS OUTPUT R = correlation between amount drunk and stupid behaviour R square = proportion of variance in outcome (behaviour) accounted for by the predictor (amount drunk) Adjusted R square = takes into account the sample size and the number of predictor variables
THE R 2
The R 2 , increases with inclusion of more predictor variables into a regression model
The adjusted R 2 however only increases when the new predictor(s) improves the model more than would be expected by chance
The adj. R 2 will always be equal to, or less than R 2
Particularly useful during variable selection stage of model building
SPSS OUTPUT Beta = standardised regression coefficient and shows the degree to which a unit increase in the predictor variable produces a standard deviation change in the outcome variable with all other things constant
REPORTING THE RESULTS OF SIMPLE REGRESSION
ß = 74, t (18) = 4.74, p < .001, R 2 = .56
Beta value t value and associate df and p R square
GENERATING DF AND T
df = n – p - 1
Where n is number of observations and
p is number of parameters estimated (i.e., predictor(s) + constant).
NB This is for regression, df can be calculated differently for other tests!
ASSUMPTIONS OF SIMPLE REGRESSION
Outcome variable should be measured at interval level
When plotted the data should have a linear trend
SUMMARY OF SIMPLE REGRESSION
Used to predict the outcome variable from a predictor variable
Used when one predictor variable and one outcome variable
The relationship must be linear
Multiple regression is used when there is more than one predictor variable
Two major uses of multiple regression:
USES OF MULTIPLE REGRESSION
Multiple regression can be used to examine the following:
How well a set of variables predict an outcome
Which variable in a set of variables is the best predictor of the outcome
Whether a predictor variable still predicts the outcome when another variable is controlled for.
MULTIPLE REGRESSION - EXAMPLE Attendance at lectures Books read Motivation Exam Performance (Grade) What might predict exam performance?