# Exercise: Multiple regression of muscle strength on age and height, 4

Question 4: Create a new variable to represent an interaction between age and height in their effects on strength. Add the interaction term to the regression.

We use Transform, Compute, to create a new variable htage = height * age.

Click Analyze, Regression, Linear. Select Quadriceps strength into Dependent and Height, Age, and htage into Independents(s). Click OK.

The fourth table of output gives the results:

Coefficients(a)
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig. 95% Confidence Interval for B
B Std. Error Beta Lower Bound Upper Bound
1

(Constant)   4660.880 1781.580     2.616   .013 1051.056 8270.704
Height (cm) -24.736 10.439 -1.440 -2.370 .023 -45.888 -3.585
Age (years) -112.751 37.067 -11.385 -3.042 .004 -187.857 -37.645
htage .647 .219 10.617 2.961 .005 .204 1.090
a. Dependent Variable: Quadriceps strength (newtons)

The interaction term is highly significant, P = 0.005, so there is strong evidence for an interaction.

The (edited) residual plots look much better:

The distribution is less skew and the plot of residual against predicted does not appear to show a relationship.

This regression model appears to be a much better fit to the data.