Correlation and Regression: The Need to Knows

Correlation is a statistical technique: tells you if scores on variable X are related to scores on variable y. Does knowing x tell you anything about y?

Correlation coefficient r: -1 ………….. 0 …………… +1

+/- 1 = perfect relationship +/- .1-.3 = weak relationship 0 = no relationship +/- .4-.6 = moderate relationship

+/- .7-.9 = strong relationship(actual # depend on what you’re studying)

The closer the data points “fit” a straight line, the stronger the linear correlation between x and y

Coefficient of determination r2 tells you how much of the variability in the the y scores in explained by variable x

typically expressed as a %

Standard error of estimation Sy.x like SEM, measures “error” by looking at the average distance points are to the line. The greater

the Sy.x, the greater the scatter and the smaller rwill be.

r = - .19

r2 = 3.5%Sy.x = 7.77

Is r weak, moderate, or strong?

How much of the variability in night fear scores is explained by age?

On average, how far is night fear scattered around the best fitting line?

df for correlation = # pairs -2

The ANOVA is not significant(p=.168) so age is probably a poor predictor of night fear.

Equation for the straight line: Y’ = bx + a

b = slope = -.181a = constant = 19.166

Y’ = a predicted value of Y fora specified value of X – use the formula!

Y’ = (-.181)(28) + 19.166 Y’ = 14.10

What would the predicted night fear score be for someone who is 28 years old?

Regression