The multiple correlation coefficient denotes the correlation between one variable and multiple other variables. It is represented as R1.234...k, where 1 is the variable being correlated and 2, 3, 4, etc. are the other variables. As an example, R1.23 would represent correlating variable 1 with variables 2 and 3 simultaneously by creating a linear combination of 2 and 3. The document then discusses using multiple correlation to correlate academic achievement with a linear combination of anxiety and intelligence.

1. Multiple correlation
coefficient
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 1

2. 1. The multiple correlation coefficient denoting a correlation of one variable with multiple
other variables.
2. The multiple correlation coefficient is denoted as R1.234...k which denotes that 1 is
correlated with 2, 3, 4, up to k variables. For example, we want to compute multiple
correlation between 1 with 2 and 3 then it is expressed as R1.23. In this case we create a
linear combination of the 2 and 3 which is correlated with 1.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 2

3. 3. We continue with the same example which we have discussed for partial and
semipartial correlations.
4. This example has academic achievement, anxiety and intelligence as three
variables.
5. The correlation between academic achievement with the linear combination of
anxiety and intelligence is multiple correlation.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 3

4. What does multiple correlation tell us?
A multiple correlation coefficient (R) yields the maximum degree of liner
relationship that can be obtained between two or more independent variables and a
single dependent variable.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 4

5. What is the difference between simple and multiple correlation?
The distinction between simple, partial and multiple correlation is based upon the
number of variables studied. When only two variables are studied it is a problem of
simple correlation. In multiple correlation three or more variables are studied
simultaneously.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 5

6. How do you correlate multiple variables?
One way to quantify the relationship between two variables is to use the Pearson
correlation coefficient, which is a measure of the linear association between two
variables. It always takes on a value between -1 and 1 where: -1 indicates a perfectly
negative linear correlation between two variables
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 6

7. What are the uses of multiple correlation?
A multiple correlation coefficient (R) yields the maximum degree of liner
relationship that can be obtained between two or more independent variables and a
single dependent variable.
Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 7

8. Dr. Ashish Suttee, M.Pharm., MBAHCS., PGD Stat., Ph.D. 8