Exercise: Muscle strength, age and height for alcoholic men, 3

Question 3: Calculate the linear regression of strength on height. Report the regression equation to a suitable number of decimal places. How does the result of the significance test of the slope of this line differ from the test for the correlation of strength and height?

Click Analyze, Regression, Linear. Select Quadriceps strength into Dependent and Height into Independent. Make sure that Method is Enter. Click OK.

You should get the following output:

Variables Entered/Removedb
Model Variables
Entered
Variables
Removed
Method
1 Height
(cm)a
Enter
a All requested variables entered.
b Dependent Variable: Quadriceps strength (newtons)

Model Summary
R Square
Std. Error of
the Estimate
1 .419a .176 .155 103.13469
a Predictors: (Constant), Height (cm)

ANOVAb
Model Sum of
Squares
df     Mean Square F Sig.
1       Regression 88510.562 1 88510.562 8.321 .006a
Residual 414833.829 39 10636.765
Total 503344.390 40
a Predictors: (Constant), Height (cm)
b Dependent Variable: Quadriceps strength (newtons)

Coefficientsa
Model Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
B Std. Error Beta
1 (Constant) -907.626 426.612 -2.128 .040
Height (cm) 7.203 2.497 .419 2.885 .006
a Dependent Variable: Quadriceps strength (newtons)

Hence the regression equation is:
quadriceps strength (N) = −908 + 7.20 × height (cm).

We do not need to report the coefficients to the same number of decimal places. I have given both to three significant figures.

The test of significance for the test of the regression slope = 0 in the population gives P = 0.006, which is identical to the test of the correlation coefficient = 0 in the population. These tests always give identical P values.