Karl pearson's correlation
- 1. CORRELATION KARL PEARSON’S COEFFICIENT CORRELATION
- 2. Intro ● Also called as “The Karl Pearson‘s product-moment correlation coefficient”. ● It is a measure of the strength of a linear association between two variables. ● denoted by r or rxy. ■ x and y being the two variables involved. ● It attempts to draw a line of best fit through the data of two variables. ● value of the Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit. ● r lies between -1 and +1, or –1 ≤ r ≤ 1, or the numerical value of r cannot exceed one (unity).
- 3. Interpretation of r. ● The value of the coefficient of correlation will always lie between -1 and +1., i.e., –1 ≤ r ≤ 1. ○ If r = +1, it means, there is perfect positive correlation. ○ If r = -1, there is perfect negative correlation. ○ If r = 0, there is no relationship between the two variables. ● It describes not only the magnitude of correlation but also its direction. ■ The degree of correlation depends upon the value. ● + 0.1 shows Lower degree of +ve correlation ● +0.8 shows Higher degree of +ve correlation. ● -0.1 shows Lower degree of -ve correlation. ● -0.8 shows Higher degree of -ve correlation.
- 4. Assumptions While calculating Karl Pearson Correlation ● There is a linear relationship (or any linear component of the relationship) between the two variables. ● We keep Outliers either to a minimum or remove them entirely. Properties of the Pearson’s Correlation Coefficient 1. r lies between -1 and +1, or –1 ≤ r ≤ 1, or the numerical value of r cannot exceed one. 2. The correlation coefficient is independent of the change of origin and scale. 3. Two independent variables are uncorrelated but the converse is not true.
- 5. Limitations ● It is not able to tell the difference between dependent variables and independent variables. ● It will not give you any information about the slope of the line. ● It only tells you whether there is a relationship.
- 6. Formula
- 7. Example 1: calculate correlation coefficient for the following data: Solution ● Calculate the sum total of x. ● Calculate the sum total of y. ● Find x2 and its sum total. ● Find y2 and its sum total. ● Calculate (x * y) and its sumtotal. ● Calculate n∑xy ● Then apply to the formula. n= number of pairs of scores/ number of variables. Here n = 6
- 8. solution
- 9. As r = -0.920, there is high degree of negative correlation.
- 10. ASSIGNMENT 1. CALCULATE THE CORRELATION OF GIVEN DATA. THANK YOU