Week 5 Exercises

Chapter 12 Review 1

(a) How does correlation analysis differ from regression analysis?

Correlation quantifies the strength of the association between two variables, but regression analysis try to find the nature of association between the variables, as well as find coefficients that show how much the dependent variable would change for unit change in the independent variable(s).

(b) What does a correlation coefficient reveal?

A correlation coefficient reveals degree of relationship between two variables. It can vary between -1 and +1. If the two variables move together in the same direction the correlation is positive and when the relation becomes perfect the value of correlation coefficient becomes +1. If the two variables move in the opposite direction the correlation is negative and it approaches -1 when the negative relation is perfect. If there is no relation between the two variables, correlation becomes zero.

(c) State the quick rule for a significant correlation and explain its limitations.

The correlation between two normal random variables is considered statistically significant if the sample correlation coefficient r is sufficiently large or sufficiently small. This is measured by the following logic:

If l r l > 2 / n ,

then the correlation is statistically significant at approximately the .05 level of significance.

For different n values the minimum required value of r for significance according to the quick rule are given below

N | R |

25 | .40 |

50 | .283 |

100 | .2 |

(d) What sums are needed to calculate a correlation coefficient?

You normally need three different sums of squares (SS). The sum of squares

for variable X, the sum of square for variable Y, and the sum of the cross-product of XY.

The sum of squares for variable X is

The sum of squares for variable Y is

The sum of the cross-product of XY is

(e) What are the two ways of testing a correlation coefficient for significance?

The t test...