Slide 1 : correlation
Definition : Definition When two variables are so related that a change in one is accompanied by a change in the other in such a way that An increase in one by an increase or decrease in other, then the variables are said to be correlated.
Slide 3 : As the winters are near my sale of woolen cloths will increase. An increase in intensity of cold results in greater sale of woollen cloths.
Types of correlation : Types of correlation Positive correlation An increase/decrease in one variable corresponds to an increase/decrease respectively in the other. Negative correlation An increase/decrease in one variable corresponds to an decrease/increase respectively in the other.
Scatter diagrams : Scatter diagrams Perfect positive correlation Perfect negative correlation High positive correlation High negative correlation No correlation
Karl Pearson's coefficient of correlation : Karl Pearson's coefficient of correlation The formula for finding the coefficient of correlation is based on the concept of co-variance If Covariance is divided by the product of individual standard deviations, the quotient so obtained is called correlation coefficient. As it was suggested by Karl Pearson so it is called Karl Pearson’s coefficient of correlation.
Another formula : Another formula If the deviation are taken from assumed mean then the formula is dx = x – A,
dy = y - B
Direct formula : Direct formula If No deviation are taken then the formula is
Interpretation : Interpretation The interpretation of r in different cases when the value of r is known is as follows:
Spearman's rank correlation coefficient : Spearman's rank correlation coefficient Untied Ranks Tied Ranks
The following table gives the test scores and sales by nine salesmen during last year in a certain firm. : The following table gives the test scores and sales by nine salesmen during last year in a certain firm. As the deviation are taken from actual mean so
Calculate the coefficient of correlation between x and y for the following data: : Calculate the coefficient of correlation between x and y for the following data: As the values are small so we can use the formula
Calculate the coefficient of correlation between the marks in English and Hindi obtained by 10 students : Calculate the coefficient of correlation between the marks in English and Hindi obtained by 10 students Taking 18 as the assumed mean for both x and y.
Calculate the Spearman's Rank Correlation coefficient between the marks in Physics and Maths. : Calculate the Spearman's Rank Correlation coefficient between the marks in Physics and Maths.
Calculate the Spearman's Rank Correlation coefficient between the heights of fathers and their sons: : Calculate the Spearman's Rank Correlation coefficient between the heights of fathers and their sons: Correction factor =