Question

Two students conduct a study to investigate the relationship between forearm length and height. Maria measures the subjects in centimeters. In a scatterplot of the data she sees a linear relationship between the variables, so she calculates the correlation coefficient. She determines that r = 0.86. John measures the same subjects in inches. He also calculates the correlation coefficient. What do you expect the correlation will be for John’s measurements?

Answer 1

Answer:

r = 0.86

Explanation:

Correlation coefficients are the strength of the relationship between two variables.

Correlations can indicate anywhere between

• 1 - for a strong positive relationship.

• -1 - for a strong negative relationship.

• 0 - for no relationship at all.

Looking at sample correlation coefficient formula which says

$r_{xy}$ = $S_{xy}$ ÷ ($S_{x}$ × $S_{y}$)

where $S_{x}$ and $S_{y}$ are the sample deviations and $S_{xy}$ is the sample covariance, all of which will remain the same for Maria and John.

Hence, John's correlation will be approximately 0.86 since he would have approximately the same measurement as Maria's measurement when Maria's measurement is converted from centimeters to inches.