Pearson’s Coefficient of correlation formula example & solution

Pearson’s Coefficient of correlation formula example & solution In statistics or quantitative methods, the Pearson correlation coefficient also known as Pearson’s r, the Pearson product-moment correlation coefficient, the bivariate correlation, or colloquially simply as the correlation coefficient is a measure of linear correlation between two sets of data. we have compiled you Pearson’s Coefficient of correlation formula, questions with solved solution to enable you understand and tackle Pearson’s Coefficient of correlation questions or exams with ease.

Definition of terms

  • How to interpret Pearson product-moment correlation: The sign (+ or -) of the correlation affects its interpretation. When the correlation is positive (r > 0), as the value of one variable increases, so does the other. 1 indicates a strong positive relationship. -1 indicates a strong negative relationship. A result of zero indicates no relationship at all.

Pearson’s Coefficient of correlation formula

r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}
r=correlation coefficient
x_{i}=values of the x-variable in a sample
\bar{x}=mean of the values of the x-variable
y_{i}=values of the y-variable in a sample
\bar{y}=mean of the values of the y-variable

Interpreting the results of Pearson’s product moment co-efficient of correlation

Correlation coefficientCorrelation strengthCorrelation type
-.7 to -1Very strongNegative
-.5 to -.7StrongNegative
-.3 to -.5ModerateNegative
0 to -.3WeakNegative
0 to .3WeakPositive
.3 to .5ModeratePositive
.5 to .7StrongPositive
.7 to 1Very strongPositive

Pearson’s Coefficient of correlation example and solutions

Example 1

The following information was extracted from the records of students showing relationship of their marks and attitude( correct X and attitude Y)

  1. Calculate the Pearson’s product moment co-efficient of correlation
  2. Interpret the result in 1 above
correct Xattitude Y

Solution 1

You will find the solution to the question above by drawing the exactly same table and adding other 5 columns for filling in values of  (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2 after filling all the values as shown below use the formula and pick the values to find your answer;

  1. Calculate the Pearson’s product moment co-efficient of correlation answer= r=0.596
  2. Interpret the result in 1 above= there is a positive weak correlation


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