Question

Explain the difference between correlation analysis and regression analysis. Give an example of a lurking variable. If a statistician computed a value of r = -2.83 what would you tell that statistician? Under what circumstances can we calculate r? Can the regression equation be assumed to hold 100 years from now? Are there other correlation coefficients other than the Pearson Product Moment Correlation Coefficient

Answer 1

Correlation analysis-

It is used to find linear relation between two random variables. Correlation analysis can be done between two random variables only.

Regression analysis-

It is used to predict a dependent variable from known values of one or more random variables. Regression analysis can be done among any number of random variables.

Example of lurking variable-

Suppose, we are considering two random variables representing number of cars in Delhi and amount (in Kg) of meat sold in Chicago. We find highly strong positive relation between these two although there is no relation among these two (nonsense correlation occurred). There is a lurking variable 'population with time'.

Validity of r = - 2.83

We know . So r = -2.83 is not valid. So we shall suggest the statistician to recheck his calculations.

Condition to calculate r-

We can calculate correlation coefficient between two random variables when some values in pairs of those two random variables are known.

Regression equation after 100 years-

Regression equation is obtained using observed data of recent times and it is used to predict expected values in near future. With time as long as 100 years, there may be drastic deviation from our calculated regression equation. So, it is not valid to use after 100 years.

Example of correlation coefficients-

There are correlations coefficients other than the Pearson Product Moment Correlation Coefficient. Some of these are as follows.

• Spearman correlation
• Kendall rank correlation
• Point-Biserial correlation