MULT30018 Lecture Notes - Lecture 5: Dependent And Independent VariablesPremium
3 pages88 viewsSpring 2018
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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.
• 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.
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'
• 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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