Researchers conducted a study of obesity in children. They measured body mass index (BMI), which is a measure of weight relative to height. High BMI is an indication of obesity. Data from a study published in the Journal of the American Dietetic Association shows a fairly strong positive linear association between mother’s BMI and daughter’s BMI (r = 0.506). This means that obese mothers tend to have obese daughters.

1. Based on this study, what proportion of the variation in the daughter BMI measurements is explained by the mother BMI measurements?
2. What are some of the other variables that explain the variability in the daughter BMI?

Part a

For this case after do the operations we got a value for the correlation coeffcient of:

With this value we can find the determination coefficient:

And with this value we can analyze the proportion of variance explained by one variable and the other. So we can conclude that 25.6% of the mother's BMI variation is explained by the daugther's BMI.

Part a

Since the BMI is a relation between height and weight, other possible variables that can explain the variability are (weight , height, age)  

Step-by-step explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

And in order to calculate the correlation coefficient we can use this formula:  

Solution to the problem

Part a

For this case after do the operations we got a value for the correlation coeffcient of:

With this value we can find the determination coefficient:

And with this value we can analyze the proportion of variance explained by one variable and the other. So we can conclude that 25.6% of the mother's BMI variation is explained by the daugther's BMI.

Part a

Since the BMI is a relation between height and weight, other possible variables that can explain the variability are (weight , height, age)  

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.