Exercise: Multiple regression of muscle strength on age and height, 5

Question 5: Try fitting a curvilinear regression using height only as a predictor. Does there appear to be evidence of a curve rather than a straight line relationship?

Suggested answer

We can do this without creating a new variable. SPSS offers a curvilinear regression option to fit curves.

Click Analyze, Regression, Curve Estimation. Select Quadriceps strength into Dependent and Height into Variable. Click Quadratic. (Linear should be checked automatically.) Click OK.

The fourth table of output gives the results:

Model Summary and Parameter Estimates
Dependent Variable: Quadriceps strength (newtons)
Equation Model Summary Parameter Estimates
  R Square F   df1   df2 Sig. Constant b1 b2
Linear .176   8.321 1 39   .006 -907.626 7.203
Quadratic .177 4.087 2 38 .025   1693.316   -23.735     .092
The independent variable is Height (cm).

The P value attached to the quadratic equation is for the whole model, not for the quadriatic part. For reasons which are not clear to me, to get this we must check the Anova box. If we do this, we get many tables, of which the last is:

t Sig.
B Std. Error Beta
Height (cm) -23.735 132.719 -1.382 -.179 .859
Height (cm) ** 2 .092 .394 1.801 .233 .817
(Constant)   1693.316   11164.107       .152     .880

"Height (cm) ** 2" is computerese for "height squared".

Now we can see that the quadratic term is not significant, P = 0.8, so there is little or no evidence for a curve.

The program also prints a scatter diagram with the straight line and quadratic curve shown. (As usual, I have edited it for legibility on a web page.)

The straight line and the curve are almost identical, which is consistent with the quadratic term being not significant.

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Last updated: 18 December, 2006.

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