Quantitative Research Methods - Correlation and Regression

Dependence and Scatter Plots

• Two or more variables are often measured on the same individuals
• Visualisation with scatter plots: one variables plotted against another, independents on the x axis and dependents on the y axis.

Relationships Between Two Variables:

• Do they co-vary/co-relate
• Do both variables move in the same diraction
• Degree or strengh of the relationship?

Co-Variance

The degree to whuch two variables vary together (in the same or opposite directions). Sum of product of residuals divided by degrees of freedom

Scaling the co-variance

Raw covariance can be any value, cannot be easily interpreted. Value scales with standard deviations. Solution:

• Scale the covariance by the standard deviation
• This yields correlation coefficent Pearson's r
• Pearson product-moment correlation coefficent

r(x,y)=  (cov(x,y) )/(SD(x)∗SD(y))

The Correlation Coefficient

Pearson Product-Moment Correlation Coefficent

• Range: between -1 and 1
• R=0 - no linear relationship between the variables, change in x is not asscoiated with change in y
• R=1 - perfect positive correlation, increase in x associated with linear increase in y
• R=-1 - perfect negative correlation, increase in x associated with linear decrease in y

Magnitude and Interpretation of r

Cohen (1988) suggested standards:

• Small - > .1-.29
• Medium - > .3-.49
• Large -> .5-1

Significance Testing for Correlation

• Distance that r must be from 0 for…