2. Correlation coefficient
• Relationship between two variables can be represented
graphically by a straight line, it is known as linear
correlation.
• Correlation can be positive, negative or zero correlation.
• Express the degree of relationship b/w two variables is
called coefficient of correlation
• -1 ( indicating perfect negative correlation) to +1 (
indicating perfect positive correlation)
• Zero means no correlation
6. Simple Correlation coefficient (r)
• It is also called Pearson's correlation or product
moment correlation
coefficient.
• It measures the nature and strength between two
variables of
the quantitative type.
• The sign of r denotes the nature of association while
the value of r denotes the strength of association.
• If the sign is +ve this means the relation is direct
• While if the sign is -ve this means an inverse or indirect
relationship
7. • The value of r ranges between ( -1) and ( +1)
• The value of r denotes the strength of the
association as illustrated
by the following diagram.
• The range of the correlation coefficient is
1 to 1. If x and y have a strong positive
linear correlation, r is close to 1
8.
9. • If r = Zero this means no association or
correlation between the two variables.
• If 0 < r < 0.25 = weak correlation.
• If 0.25 ≤ r < 0.75 = intermediate correlation.
• If 0.75 ≤ r < 1 = strong correlation.
• If r = l = perfect correlation.
10. Multiple Correlation
• If a variable is dependent on a number of
other variables called independent variables.
• Ex:
Academic
Achievement
Intelligence
Teaching
Methods
Parents
Education
12. Regression
• The coefficient of correlation tells us the way in
which two variables are related to each others.
• Coefficient of correlation b/w two variables
cannot predict the change in one variable in
systematic way, with the change in the other
variable.
• Regression help in the task of prediction.
• The process of predicting variable Y using
variable X
• Tells you how values in y change as a function of
changes in values of x
13. Coefficient of Determination
• The coefficient of determination r2 is the ratio
of the explained variation to the total variation.
That is,
•
Example:
The correlation coefficient for the data that
represents the number of hours students watched
television and the test scores of each student is r =
0.831. Find the coefficient of determination.
•
2 Explained variation
Total variation
r
2 2
( 0.831)
r 0.691
14. Uses of Regression Analysis
• Regression analysis helps in establishing a
functional relationship between two or more
variables.
• Since most of the problems of psychology
analysis are based on cause and effect
relationships, the regression analysis is a highly
valuable tool in education and psychology
research.
• Regression analysis predicts the values of
dependent variables from the values of
independent variables
15. Simple Regression
• A statistical model that utilizes one
quantitative independent variable “X” to
predict the quantitative dependent variable
“Y.”
• Tells you how values in y change as a
function of changes in values of x
80
100
120
140
160
180
200
220
60 70 80 90 100 110 120
Wt (kg)
SBP(mmHg)
16. Multiple Regression
• A statistical model that utilizes two or more
quantitative and qualitative explanatory
variables (x1,..., xp) to predict a quantitative
dependent variable Y.
• Multiple regression analysis is a
straightforward extension of simple regression
analysis which allows more than one
independent variable
17. R Squared
•R-squared is the percentage of the response variable
variation that is explained by a linear model. Or:
•R-squared = Explained variation / Total variation
•R-squared is always between 0 and 100%:
• 0% indicates that the model explains none of the
variability of the response data around its mean.
• 100% indicates that the model explains all the
variability of the response data around its mean.
18. • The standard error measures the scatter in the
actual data around the estimate regression line.
• Standard Error is calculated by taking the
square root of the average prediction error.
• Standard Error = SSE
• n-k
• Where n is the number of observations in the
sample and k is the total number of variables in
the model
Standard Error of Regression
