Answer:
The value of r is always between
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.
Step-by-step explanation:
For this case we know that the correlation between the height and weight of children aged 6 to 9 is found to be about r = 0.8. And we know that we use the height x of a child to predict the weight y of the child
We need to rememeber that the correlation is a measure of dispersion of the data and is given by this formula:
The value of r is always between
And we have another measure related to the correlation coefficient called the R square and this value measures the % of variance explained between the two variables of interest, and for this case we have:
So then the best conclusion for this case would be:
c. the fraction of variation in weights explained by the least-squares regression line of weight on height is 0.64.