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Statistical modelling/Multiple regression analysis |
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Note that the residual degrees of freedom in the regression analysis are 45. The corresponding number in the earlier polynomial analysis of variance was 35. Why is this? The respective residual mean squares are 102.7 (here) and 95.87 (earlier). Again why? The reason is that the analysis of variance model included 5 degrees of freedom for length and bud within length and 7 for sucrose concentration. In the regression analysis the effect of bud and bud length has been ignored and only two degrees of freedom have been used to describe the relationship with sucrose concentration. |
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The fact that the residual mean squares are very close implies that the fitting of the reduced model has had little impact on the size of the standard errors. To make a simple adjustment to allow for the difference in residual mean square, however, the following calculation can be made. Adjusted s.e. = s.e. x |
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with 95.87 the value of the earlier residual mean square.
For example, the revised s.e. for constant term = 3.48 x 
