Correlation measures the degree of interdependence (association) between two variables. If two variables are so related that an increase or decrease of one is found in connection with increase or decrease of the other, then the two variables are said to be correlated. Here it is important to note that there might be a similar movement between two variables such as automobile sales and demand for shoes. But these two variables have no connection due to which the calculation for these two variables is wrong because it does not make any sense. Therefore care must be taken that the two variables have some connection before a calculation can make sense.
Correlation Coefficient
The correlation coefficient gives a mathematical value for measuring the strength of the linear relationship between two variables.
r lies between -1 and +1
- +1 indicates perfect positive relation
- -1 indicates perfect negative relation
- 0 shows no correlation
Calculation of Correlation Coefficient
The formula for calculating linear correlation coefficient is called product-moment formula presented by Karl Pearson. Therefore it is also called Pearsonian coefficient of correlation. The formula is given as:
Note: Correlation is the geometric mean of absolute values of two regression coefficients i.e.
Scatter Diagrams for different degrees of correlation
I go through ur correlation & regression chapters but i did not find derivation of any formula. i would like to know the derivation of all formulas. would u pleasure to tell the above
In the case of ‘r’ taking a negative value, how can I interpret the Probable error value i.e say I get ‘r’= -0.89 & using the formula indicated I get a value of 0.0625 for the P.E (which is positive), how do I interpret the significance of the ‘r’ value. Just because r<P.E in this case does it cease to be significant-in which case all negative values of 'r' will not be significant, isn't it?
Does a 0.9 coefficient imply that sales increase by 90% if advertising expenditure increases by 100%?
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