Question

Suppose that the regression for predicting weight (in pounds) from Height (in Select one answer inches) is given by Weight =-115 + 3.6(Height) Which of the following statements is correct? I. A person who is 61 inches tall will weigh 104.6 pounds II. For every additional inch of height, the predicted weight will increase, on average, by 3.6 pounds. III. The correlation between weight and height is negative. ı points A. I only B. II only C. III only D. O I and II only E. II and III only

Answer 1

Answer:

Option D)  I and II only                                    

Step-by-step explanation:

We are given the following in the question:

Regression equation:

$w = -115 + 3.6h$

where w is the weight in pounds and h is the height in inches.

Since the weight depends on height, height becomes the independent variable and weight becomes the dependent variable.

I. A person who is 61 inches tall will weigh 104.6 pounds

When h = 61,

$w = -115 + 3.6(61) = 104.6$

Thus, the given statement is true.

II. For every additional inch of height, the predicted weight will increase, on average, by 3.6 pounds.

If the height increases by 1 unit, then,

$w(h+1) - w(h) = -115 + 3.6(h+1) - (-115 + 3.6(h))\\w(h+1) - w(h) = 3.6(h+1-h)\\w(h+1) - w(h) = 3.6$

Thus, the given statement is correct.

III. The correlation between weight and height is negative.

No, the given statement is not correct as with increase in height the weight increases and with decrease in height the weight decreases.

Thus, the correct answer is

Option D)  I and II only