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Tutor, please explain in details. Thanks! We measured the HEIGHT and WEIGHT for each of the 100 children randomly selected from a certain population. The

Tutor, please explain in details. Thanks!

We measured the HEIGHT and WEIGHT for each of the 100 children randomly selected from a certain population. The sample variance of HEIGH and WEIGHT are 400 and 100, respectively.

The sample correlation coefficient between HEIGHT and WEIGHT is 0.7.

1. IS the population correlation coefficient between HEIGHT and WEIGHT equal to 0.6 or not? Justify your statement formally.

2. Suppose we are running a regression using the model HEIGHT = a+ b *WEIGHT. Calculate the least-square estimate of b.

3. What is the proportion of the variance of HEIGHT that is explained by WEIGHT in the above regression?

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