Supplementary Exercise 11.15 of IPS7e: -------------------------------------- Minitab commands and output: --- WOpen "R:\Chapter 11\ex11_015.mtw". Correlation 'GPA'-'Age' 'SC'-'C6'. Correlations: GPA, IQ, Age, SC, C1, C2, C3, C4, C5, C6 GPA IQ Age SC C1 C2 C3 C4 C5 IQ 0.634 0.000 Age -0.389 -0.382 0.000 0.001 SC 0.542 0.493 -0.178 0.000 0.000 0.119 C1 0.441 0.222 -0.212 0.697 0.000 0.051 0.062 0.000 C2 0.601 0.547 -0.248 0.846 0.624 0.000 0.000 0.028 0.000 0.000 C3 0.495 0.441 -0.111 0.800 0.368 0.692 0.000 0.000 0.333 0.000 0.001 0.000 C4 0.267 0.234 0.006 0.781 0.382 0.592 0.609 0.018 0.039 0.957 0.000 0.001 0.000 0.000 C5 0.472 0.347 -0.123 0.778 0.404 0.614 0.736 0.689 0.000 0.002 0.283 0.000 0.000 0.000 0.000 0.000 C6 0.401 0.360 -0.041 0.839 0.516 0.623 0.732 0.727 0.716 0.000 0.001 0.721 0.000 0.000 0.000 0.000 0.000 0.000 Cell Contents: Pearson correlation P-Value Comments and answers to questions: ---------------------------------- The correlations with GPA are given in the first column of the matrix above. Strictly speaking it is not meaningful to compute a correlation involving the categorical variable Sex, although the resulting correlation can be interpreted in terms of the R2 of a two-sample model. Among the rest, IQ has the strongest correlation with GPA and would therefore have the strongest association with GPA in a simple linear regression (recall that the tests for zero correlation and zero slope are identical!). The R^2 for the simple linear regression with IQ would be: R^2 = 0.634^2 = 0.402 = 40.2%.