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?

Suggested answer

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
Model	R	R Square	Adjusted 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.

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