Question

00 00 00 y 5.16-0.06*x 00 00 00 30.00 25.00 20.00 15.00 10.00 5.00 00 Knee Extension Strength O

A physical therapist wants to examine a relationship between falls and knee extension strength in the elderly. Further, he would like to predict falls with knee extension strength in the elderly. I ran a scatterplot (see above). Does this mean I can use simple linear regression?

Answer 1

From the visual examination, it appears that the data values are clustered around the central line on either side, though not very close to the central line.

For getting precise decision whether we can use linear regression, the following steps are to be carried out:

(1) Calculate Linear Correlation Coefficient (r) between x and y: The absolute value of Correlation Coefficient (r) should be close to 1 to confirm that linear relation exists. If it is near 0, it means x and y are nearly independent.

(2) Hypothesis Test for the Population Correlation Coefficient ($\rho$) is to be done as follows:
H0: Null Hypothesis: $\rho$ = 0

HA: Alternative Hypothesis: $\rho \neq$ 0.

The result of the Hypothesis Test should be to reject Null Hypothesis so that linear relation between x and y is confirmed.