1. (a) How does correlation analysis differ from regression analysis? Correlation analysis identifies the relationship between independent and dependent variables while regression analysis uses independent variables to predict dependent variable by means of predictive model.
(b) What does a correlation coefficient reveal?
Correlation coefficient reveals the degree of association between independent and dependent variables. The closer to the one the value is the more strong relationship. Negative values means negative relationship with r=-1 as perfect negative relationship whereas positive values means positive association with perfect positive association as r=1.
(c) State the quick rule for a significant correlation and explain its limitations.
r=1 means perfect positive relationship r=-1 means perfect negative relationship r=0 means no relationship
Limitations are with respect to its subjectivity because r slightly greater than 0.5 may be treated as good relationship whereas r slightly less than 0.5 may have opposite meaning.
(d) What sums are needed to calculate a correlation coefficient?
Sums required are:
1) −(−)
2) (−)2
3) (−)2
(e) What are the two ways of testing a correlation coefficient for significance?
Two methods are:
1) t-test: The test statistic is:=−21−2
2) z-test: Test statistic is:=ln[+1−1]2
12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees.
(a) Write the fitted regression equation.
The regression equation is:
=30.7963+0.0343
(b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05.
(c) The degrees of freedom as shown in the output is 33
The critical value at =0.05 is 2.035
