bi/b1
- Regression coefficient for the predictor
- Gradient (slope) of the regression line
- Direction/strength of relationship
b0
- Intercept (value of Y when X = 0)
* Point at which the regression line crosses the Y-axis (ordinate)
The F test
How much the model has improved the prediction of the outcome
If F is high, it means that…
that the model means something, if not, you can just use the mean
R^2
Indicates how much variation of a dependent variable is explained by the independent variable(s) in a regression model.
Only important if we want to do predictions
R^2 high or low?
If high, we explain relatively much of this variation and why (in our outcome variable)
If low, not so much of the variation in why
Interpretation of 𝜷𝑖 coefficients is “ceteris paribus”
other things equal
OLS assumptions
- A 1: The regression model is linear in the coefficients and error term.
- A 2: Error term has a mean value of zero.
- A 3: All independent variables are uncorrelated with the error term (aka exogeneity assumption). This one is almost never met, for reasons of confounding factors such as unobserved variable bias or simultaneity bias.
- A 4: Observations of the error term are uncorrelated with each other.
- A 5: Error term has a constant variance (is homoscedastic, not heteroskedastic).
Dependent t-test
- Compares two means based on related data.
- E.g., Data from the same people measured at different times.
- Data from ‘matched’ samples, they’re sometimes referred to as “matched-pairs” test or “paired t-test”.
Independent t-test
- Compares two means based on independent data.
- E.g., data from different groups of people.
- Sometimes referred to as two-sample t-test.
Both the independent t-test and the dependent t-test are parametric tests based on the normal distribution. Therefore, they assume:
• The sampling distribution is normally distributed. In the dependent t-test this means that the sampling distribution of the differences between scores
should be normal, not the scores themselves.
• Data are measured at least at the interval level.
The independent t-test, because it is used to test different groups of people, also assumes:
- Variances in these populations are roughly equal (homogeneity of variance).
- Scores in different treatment conditions are independent.
Effect Size Measures
r = .1 / .3 / .5
r = .1 (small effect):
• the effect explains 1% of the total variance.
r = .3 (medium effect):
• the effect accounts for 9% of the total variance.
r = .5 (large effect):
• the effect accounts for 25% of the variance.
Beware of these ‘canned’ effect size though
• The size of effect should be placed within the research context.
