# MULT30018 Lecture Notes - Lecture 5: Dependent And Independent VariablesPremium

3 pages98 viewsSpring 2018

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**preview**shows half of the first page. to view the full**3 pages of the document.**WEEK 5 – REGRESSION ANALYSIS

Y = a + bx + e (1 independent variable)

Y = a +bx1 + bx2 + e (2 independent variable) and so on…

• Every unit increasing in x makes the Y go up or down by that amount.

• Tells the magnitude of the effect

Regression with one variable

R^2 tells us the variation percentage

1. Regression Coefficient (b) and p value (sig.)

2. The r squared statistic

3. ANOVA test (esp. check df=N)

4. Remember, multiple regression gives us a way to statistically deal with the 'third factors' we

have been talking about in previous weeks.

Some caveats

• Something being 'statistically significant' (sig = 0.05) does not mean the result is 'significant'

• Dependent variables must have 3+ categories

• And these must make sense numerically

• Think before choosing dependent and independent variables

Correlation vs. Regression

• Correlation shows the correlation (-1 - +1) between two variables (it is a summary measure)

• Regression tells us about the magnitude of the effect of one or more independent variables on

a dependent variable.

Linear Regression

Why do we use regression?

• Correlation tells us the degree to which two variables are associated, or how well a line can

describe the relationship between two variables. It shows us how well two variables 'track'

one another

• A high r tells us that the values of two variables are closely associated, but it does not allow us

to predict the value of one if we know the value of another

• Regression allows us to estimate the value of one variable if we know the value of another

• It does this by providing the 'regression line', which allows us to see the expected change in

one variable which corresponds with change in another

• Regression line shows us the patterns in our data

• Regression tells us how much change in one variable is associated with another, correlation

just tells us how closely they are associated.

The regression equation : Y = a + bx

• The regression eqution is simply the formula for a straight line

• Y is the value of the DV

• X is the value of the IV

• 'a' is the constant or y-intercept. It is the value of y when x=0 (where the line 'starts').

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