What is Karl Pearson’s Coefficient of Correlation?

Coefficient of Correlation

A correlation coefficient is generally applied in statistics to calculate a relationship between two variables. The correlation shows a specific value of a degree of a linear relationship between X and Y variables. There are various types of a correlation coefficient, but Pearson’s correlation (also called Pearson’s R) is the correlation coefficient frequently used in linear regression.

Pearson’s Coefficient Correlation

Karl Pearson’s Coefficient of Correlation is an extensively used mathematical method in which the numerical representation is applied to measure the level of relation between linear related variables. The coefficient of correlation is expressed by “r”.

Karl Pearson Correlation Coefficient Formula

Alternative Formula (covariance formula)

Pearson correlation example

  • When a correlation coefficient is (1) that means every increase in one variable, there is a positive increase in other fixed proportion. For instance, shoe sizes change according to the length of the foot and are (almost) perfect correlation.
  • When a correlation coefficient is (-1) that means every positive increase in one variable, there is a negative decrease in other fixed proportion. For instance,with the decrease in the quantity of gas in a gas tank, it shows (almost) a perfect correlation with speed.
  • When a correlation coefficient is (0) for every increase, it means there is no positive or negative increase and the two variables are not related.

DIY Questions

ACTUAL MEAN METHOD

Q.1 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USING ACTUAL MEAN METHOD).
Price (`) 10 20 30 40 50 60 70
Supply (Units) 8 6 14 16 10 20 24
Q.2 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USE ACTUAL MEAN METHOD).
X 15 18 20 28 34
Y 40 42 46 50 52

ASSUMED MEAN METHOD

Q.1 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USING ASSUMED MEAN METHOD).
Price (`) 10 20 30 40 50 60 70
Supply (Units) 8 6 14 16 10 20 24
Q.2 FROM THE FOLLOWING DATA COMPUTE CORRELATION BETWEEN HEIGHT OF FATHER AND HEIGHT OF DAUGHTERS BY KARL PERASON’S COEFFICIENT OF CORRELATION. (USING ASSUMED MEAN METHOD).
Height of Father (Cms) 65 66 67 67 68 69 71 73
Height of Daughter (Cms) 67 68 64 69 72 70 69 73

STEP DEVIATION METHOD

Q.1 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USING STEP DEVIATION METHOD).
Price (`) 10 20 30 40 50 60 70
Supply (Units) 8 6 14 16 10 20 24
Q.2 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USE STEP DEVIATION METHOD).
Density (Per Sq. Km) 2000 5000 4000 7000 6000 3000
Patients of dengue fever 100 160 140 200 170 130

DIRECT METHOD

Q.1 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USING DIRECT METHOD).
Price (`) 10 20 30 40 50 60 70
Supply (Units) 8 6 14 16 10 20 24
Q.2 FROM THE FOLLOWING DATA COMPUTE KARL PERASON’S COEFFICIENT OF CORRELATION. (USING DIRECT METHOD).
Price (in `) 5 6 3 4 3
Demand (in Units) 10 10 12 11 12

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