Chapter 7. Correlation, Bivariate Regression, and Multiple Regression. Pearson’s Product Moment Correlation. Correlation measures the association between two variables. Correlation quantifies the extent to which the mean, variation & direction of one variable are related to another variable.
Correlation, Bivariate Regression, and Multiple Regression
y = 0.5246x - 2.2473
R2 = 0.4259
y = 0.0012x - 1.0767
R2 = 0.0035
If N is large (N=90) then a .205 correlation is significant.
ALWAYS THINK ABOUT R2
How much variance in Y is X accounting for?
r = .205
R2 = .042, thus X is accounting for 4.2% of the variance in Y.
This will lead to poor predictions.
A 95% confidence interval will also show how poor the prediction is.
R2=.64 (64%) Variance in Y that is explained by X
Unexplained Variance in Y. (1-R2) = .36, 36%
The vertical distance (up or down) from a data point to the line of best fit is a RESIDUAL.
r = .845
R2 = .714 (71.4%)
Y = mX + b
Y = .72 X + 13
The SEE is the SD of the prediction errors (residuals) when predicting Y from X. SEE is used to make a confidence interval for the prediction equation.
Enter the variables
Click Statistics Button
71.5% percent of the variance in Y is explained by X.
Correlation (r) r = .845 between X and Y.
Y = .726 (X) + 12.859
Y = .726 (X) + 12.859 ± 1.96 (6.06)
Both r and SDY are critical in accuracy of prediction.
If SDY is small and r is big, predictions are will be small.
If SDY is big and r is small, predictions are will be large.
We are 95% sure the mean falls between 45.1 and 67.3
Each variable accounts for unique variance in Y
Very little overlap of the predictors
Order to enter?
X1, X3, X4, X2, X5