Correlation is a measure of relationship between two variables. The two variables must be numeric or scale. So basically correlation is applied on the quantitative variables.

### Correlation Coefficient

Correlation Coefficient gives the mathematical value for measuring the strength of the linear relationship between two variables. It ranges from -1 to +1.

• +1 representing absolute positive linear relationship (X increases, Y increases).

• -1 representing absolute inverse relationship (X increases, Y decreases).

• 0 representing no linear relationship (X and Y have no pattern).

### Bivariate Correlation

Bivariate Correlation tests the strength of the relationship between two variables without giving any consideration to the interference some other variable might cause to the relationship between the two variables being tested.

### Partial Correlation

It allows us to examine the correlation between two variables while controlling for the effects of one or more of the additional variables without throwing out any of the data.

**Please Note that:**

• One-tailed test is appropriate if we are making predictions about a positive or negative relationship between the variables.

• Two-tailed test should be used if there is no prediction bout the direction of relation between the variables to be tested.

The null hypothesis for both bivariate and partial correlation is same and is given below.

**Ho:** There is no correlation between the given variables.

**Note:** Reject the null hypothesis if P value (two-tailed) corresponding to the correlation coefficient is less than 0.05 at 5% significance level.

### Correlation Examples

A student of economics is interested to know whether there is a correlation between price and quantity demanded. For this purpose he took a sample of 10 years containing data of aggregate demand and general price level. The data is given in the SPSS file with the name of price. Please check whether there is a correlation between price and quantity demanded.

A) Researcher only wants to check the relation between price and demand.

B) Researcher is also interested to know the impact of some other variables like discounts.

**Solution (A)**

If the researcher is only interested to check the correlation between price and demand then he can use Bivariate correlation. The null hypothesis for bivariate correlation is given below.

Ho: there is no correlation between price and quantity demanded.

The above table shows that correlation between price and quantity demanded. The coefficient of correlation is -0.991 corresponding to the sig value (2 tailed) of < 0.0001. Since the sig value is less than 0.01 we can reject the null hypothesis and conclude that there is strong negative correlation between price and quantity demanded.

**Solution (B)**

If the researcher is also interested to know the impact of discounts on the quantity demanded then he can use partial correlation for this purpose. For this purpose a null hypothesis is constructed which is given below.

**Ho:** There is no correlation between the price and quantity demanded while controlling for the effect of discounts.

The above table shows correlation between price and quantity demanded while controlling for the effect of discounts. The value of coefficient of correlation is 0.612 and the sig value (2-tailed) is 0.080. Since the value of P is greater than 0.05 therefore we accept the null hypothesis and conclude that quantity demanded is not significantly related to the price.