Correlation and Regression

Correlation analysis

• method used to measure the strength of relationship between two or more variables,

• positive correlation

• Negative correlation

• Zero correlation

Types of correlations

Positive correlation 

• exists when high scores in one variable are associated with high scores in the second variable

Negative correlation

• exists when high scores in one variable are associated either with low scores in the second variable

ZERO CORRELATION

• exists when high scores in one variable tend to score neither systematically high nor systematically low in the other variable.

Scatter Diagram

A graph of plotted points that shows the

relationship between two sets of data.

Perfect correlation= 1.0

high= 0.80-0.99

moderately high= 0.60-0.79

Moderate= 0.40-0.59

Low=  0.20-0.39 

Slight/negligible=0.01-0.19

No correlation= 0

Perfect correlation=

high=

moderately high=

Moderate=

Low=

Slight/negligible=

No correlation=

PEARSON PRODUCT-MOMENT CORRELATION COEFFICIENT

The most common statistical tool in

measuring the linear relationship between

two random variables,

Pearson Product-Moment Correlation Coefficient or Pearson r

x and y, is the linear

correlation coefficient commonly called

the ____________ or _________for short.

KARL PEARSON

x and y, is the linear

correlation coefficient commonly called

the Pearson Product-Moment Correlation

Coefficient or Pearson r for short. This

formula was developed and perfected by

__________

Pearson Product-Moment Correlation

Coefficient FORMULA:

TEST OF SIGNIFICANT OF THE CORRELATION COEFFICIENT

 It is important that the value of the

correlation coefficient be tested if it is

significant or not. If it is found to be

significant then, there is a relationship that

exists between the two variables.

Otherwise, the computed r is due to

chance alone.

SPEARMAN RANK-ORDER CORRELATION

COEFFICIENT

The Pearson product-moment correlation

coefficient is most appropriate when the

data are interval or ratio scale. For ordinal

data, the ___________of the ranks of the variables is

used to determine the strength of

relationship between two variables.

FORMULA OF Spearman Rank-Order Correlation Coefficient

REGRESSION ANALYSIS

 deals with the estimation of one variable

based on the changes or movements of the

other variable.

y=a + bx

formula of regression analysis

y= criterion measure

x= predictor

a= ordinate or point where the regression line corsses the y-axis

b=beta weight of the slope of the line

y=

x=

a=

b=