Question

A group of researchers were studying the weight of young girls from ages 10-14 and then created a model to explain the relationship of weight and age:

Weight = B0 + B1*Age + E

1) In the following model, what does B0 represent?

Weight = B0 + B1*Age + E

Group of answer choices

2) In the following model, interpret B1 if B1 equals 7 pounds?

Weight = B0 + B1*Age + E

Choose the best, most complete answer.

We expect the average weight of girls at any age to increase by 7 pounds for a one-year increase in age.

We expect the average weight of girls between the ages of 10 and 14 to increase by 7 pounds for a one-year increase in age.

We expect the weight of girls at age 10 to increase by 7 pounds for a one-year increase in age.

Girls between the ages of 10 and 14 will increase in weight by at most 7 pounds since we didn't account for height.

3)A group of researchers were studying the weight of young girls from ages 10-14 and then created a model to explain the relationship of weight and age:

Weight = B0 + B1*Age + E

Researchers found that age and weight had a correlation of .50.

True or False: This means that age and weight have a weak linear relationship.

4) A group of researchers were studying the weight of young girls from ages 10-14 and then created a model to explain the relationship of weight and age:

Weight = B0 + B1*Age + E

Researchers found that age and weight had a correlation of .50.

What would R^2 equal and how would you interpret it?

Answer 1

1) Here the model is Weight = B0 + B1* Age + E

The B0 is the intercept which represents the amount of units shifted from the origin either in the left or the right direction .

2)  In the following model we have to  interpret B1 if B1 equals 7 pound .

Weight = B0 + B1*Age + E

The anwer is the second option i.e,

We expect the average weight of girls between the ages of 10 and 14 to increase by 7 pounds for a one-year increase in age.

3)A group of researchers were studying the weight of young girls from ages 10-14 and then created a model to explain the relationship of weight and age:

Weight = B0 + B1*Age + E

Researchers found that age and weight had a correlation of .50.

This is False. This doesnot means that age and weight have a weak linear relationship since 0.50 correlation indicates moderately good linear relationship.

4) A group of researchers were studying the weight of young girls from ages 10-14 and then created a model to explain the relationship of weight and age:

Weight = B0 + B1*Age + E

Researchers found that age and weight had a correlation of .50.

Hence here R2 = 50%.

From the obtained value of R2 we can say that 50% of total variation has been explained by the regression equation of weights on age. As such we may conclude that the regression equation is quite useful as a prediction formula.