Linear CorrelationA linear correlation◦ relationship between two variables that shows up on a scatter diagram as dots roughly approximating strai ht a ro imatin a straight line
Curvilinear Correlation Curvilinear correlation ◦ any association between two variables other than a linear correlation ◦ relationship between two variables that shows up on a scatter diagram as dots following a systematic pattern that is not a straight line
The Correlation Coefficient(r) The sign of r (Pearson correlation coefficient) tells the general trend of a relationship between two variables. + sign means the correlation is positive. - sign means the correlation is negative. The value of r ranges from -1 to 1. A correlation of 1 or -1 means that the variables are perfectly correlated. 0 = no correlation
Strength of Correlation CoefficientsCorrelation Coefficient Value Strength of Relationship+/- .70-1.00 Strong g+/- .30-.69 Moderate+/- .00-.29 None (.00) to Weak The value of a correlation defines the strength of the correlation regardless of the sign sign. e.g., -.99 is a stronger correlation than .75
The Statistical Significance of a CorrelationCoefficientA correlation is statistically significant if it isunlikely that you could have gotten acorrelation as big as you did if in fact therewas no relationship between variables. p◦ If the probability (p) is less than some small degree of probability (e.g., 5% or 1%), the correlation is considered statistically significant.
The Correlation Coefficient and theProportion of Variance Accounted forP fV A dfProportion of variance accounted for (r2)◦ To compare correlations with each other, you have to square each correlation correlation.◦ This number represents the proportion of the total variance in one variable that can be explained by the other variable.◦ If you have an r= .2, your r2= .04 r◦ Where, a r= .4, you have an r2= .16◦ So, relationship with r = .4 is 4x stronger than , p g r=.2