Correlation & Regression Flashcards
How do we get the proportion of explained variance from two continuous variables?
Correlate the two variables and square it
Why can’t we just use covariance?
Not standardised
what do you have to do to a correlation first in order to test for significance?
Convert to a t score
What does 1 - r^2 represent?
unexplained variance
What does a partial correlation do?
Examines the correlations between variables x, y and a confound z in order to remove or control for the variable z
What differences are there between a partial correlation and a covariance analysis
In C.A the independent variables are categorical.
ANCOVA is also a linear model while P.C is using correlations
What do the B’s stand for in model’s?
Parameter estimates
What assumptions does regression operate under?
Sensitivity (to outliers)
Homoscedasticity ( variance of residuals should be equal across all expected values)
What can be used in order to control for outliers? (3)
Cook’s distance (<1)
Mahalonobis (<11 at N= 30)
Laverage ( The average leverage value is defined as (k + 1/n)
How do you test for homoscedacticity?
Look at scatterplot of standardised: expected values x residuals. Roughly round shape is needed
In the equation for regression, what does b1 represent?
The regression slope
In the equation for regression, what does b0 represent?
The intercept of the regression slope and the y axis
What t test is used for regression?
One sample t test of b1
What is meant by the covariance?
the averaged sum of combined deviations.
What formulas can be used in r for correlations and covariances?
- cor(x, y, “everything”, “pearson”)
* cov(x, y, “everything”, “pearson”)
How do you calculate a correlation in spss?
Go to analyze > correlate > bivariate. Enter the variables in variables. You can choose which correlation coefficients you want: Pearson, Kendall’s tau-b, or Spearman.
How do you calculate a partial correlation in spss?
Go to analyzeàcorrelateàpartial. Place the variables under variables and the variable you want to control for under controlling for. Click on optionsàzero-order correlations to get the r that you would get if you didn’t control for the third variable.
What is meant by simple linear regression?
regression with one continuous independent variable and one continuous dependent variable. It is used to see if you can predict the values of the dependent variable using the independent variable.
What might the hypotheses for a simple linear regression look like?
- H0:X can’t predict Y; b1 =0; t=0; orF=0
* Ha: X can predict Y; b1 0; t 0; orF>0
How are the degrees of freedom calculated in linear regression?
df = n - p - 1
- n = the number of entities
- p = the number of predictors
How do we calculate the fit of the model?
To test the fit of the model we can perform an F-test.
n-p-1)r^2 / p(1-r^2
What would an R^2 of 37.4 in the spss output mean?
x can account for 37.4% of the variance in y
How do you calculate a linear regression in spss?
Go to analyze > regression > linear. Place the dependent variable in dependent and the independent variable in independent(s).
Under statistics we select model fit, R squared change, descriptives, part and partial correlations and collinearity. Under save we tick mahalanobis, Cook’s and leverage values to get an idea of extreme outliers in the data. It’s also good to tick unstandardised under predicted values, to see what the expected value in the data set is.
