You have reason to believe that Gender is related to the Sta

You have reason to believe that Gender is related to the Starting Salary and Work Experience of graduates. Based on the results below, would your beliefs be supported? Explain your reasoning.

                                                                      Correlations

Gender

Starting Salary

Work Experience

Gender

Pearson Correlation

1

.160(**)

.361(**)

.

.000

.000

1100

1100

1100

Starting Salary

Pearson Correlation

.160(**)

1

.367(**)

.000

.

.000

1100

1100

1100

Work Experience

Pearson Correlation

.361(**)

.367(**)

1

.000

.000

.

1100

1100

1100

** Correlation is significant at the 0.01 level (2-tailed).

Examine the output below and indicate which of the two predictors is better at predicting starting salary? How did you reach your conclusion?

Given the information below (adapted from the salary data above):

Model (regression) sum of squares = 985,000               N (sample size) = 1100

Error (residual) sum of squares = 6,265,000 k (predictors) = 2

Calculate the value of R-squared for this model (to four decimal places).

What are the degrees of freedom for the F statistic associated with the above.

                Numerator df: Denominator df:

3. What is the average leverage of all cases in this model (to four decimal places)?

Solution

Given r₁₂=r₂₁=160, r₁₃=r₃₁=361, r₂₃=r₃₂=367. H0: Correlation is not significant against H1:Correlation is significant .

r_13.2=[r₁₃-(r₁₂r₃₂)]/[(1-(r₁₂)²)(1-(r₃₂)²)]=[361-(160*367)]/[(1-(160)²)(1-(367)²)]=-0.9939, then t=[r_13.2(N-2)]/[1-(r_13.2)²]=(-0.9939*33.1361)/0.1104=-298.3149<2.58(Z table value at 0.01 level of significance for large sample). So we accept null hypothesis. Therefore, Ho: Correlation is not significant.

R-squared = 1-[RSS/TSS]=1-[985000/6265000]=1-0.1572=0.8427.