I am setting up a linear analysis of a single continuous dependent variable, with multiple (up to 11!) continuous independent variables. I am interested in doing something like an ANCOVA that will show the relative contribution and co-variation among the variables. But my understanding is that ANCOVA requires having at last one categorical variable, which my data does not have. I have already done multiple regression analysis that yields a correlation grid, but does not show covariation among variables. Is there another analysis I should consider? Should I force my data to fit into an ANCOVA analysis?

Here's a sample of the data for clarity.

DV      iv1     iv2     iv3     iv4     iv5     iv6
-0.34   2.05    7.77    0.00    3.91    2.23    10.80
-0.40   2.23    0.53    3.14    1.67    3.34    13.93
-0.24   6.98    2.04    2.82    9.30    2.33    13.95
-0.39   0.00    1.48    0.00    2.62    3.06    10.04
-0.32   0.79    0.00    0.00    5.51    3.94    10.24
0.24    0.00    0.00    0.00    0.00    6.15    13.85
1.58    1.34    0.00    0.00    3.41    2.20    13.05
1.07    4.05    2.99    0.00    2.89    3.47    8.09
-0.44   2.31    1.86    0.00    1.54    4.62    13.08
-0.49   2.94    2.68    0.00    10.29   1.47    11.76
  • $\begingroup$ Just for clarity - do you mean you'd like to see the covariation among the variables or among the coefficient estimates? $\endgroup$ – jbowman Dec 7 '11 at 22:30
  • $\begingroup$ @jbowman I might not fully understand the distinction, but the latter (covariation among coefficient estimates of each IV) is what I had in mind. Could you explain the distinction between the two? $\endgroup$ – ted.strauss Dec 7 '11 at 23:05
  • 3
    $\begingroup$ Covariation among the variables is the covariance of the columns of the X matrix in the regression, i.e., your $iv1 \dots iv6$ variables in your data sample. The covariance of the coefficient estimates is the covariance between $\hat{\beta}_0 \dots \hat{\beta}_6$ ($\hat{\beta}_0$ being the estimate of the constant term.) The vcov function applied to the result of your regression (vcov(lm(dv+iv1+iv2+iv3+iv4+iv5+iv6)), for example) will give you the covariance matrix of the parameter estimates. $\endgroup$ – jbowman Dec 8 '11 at 1:11

You said you want "the relative contribution and co-variation among the variables." Multiple regression can give you what you're looking for, if you take advantage of what it has to offer. A correlation matrix is a very small part of what regression can yield. Assuming the predictors are relatively independent--which can be tested using tolerance or variance inflation factor statistics from a regression--the strength of the standardized coefficients will indicate the strength of each predictor's association with the outcome. T-statistics and partial and semipartial correlations can add information about this as well.


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