Question

Suppose that the regression for predicting weight (in pounds) from Height (in 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 poulds.
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.
A. II only
B. Iand II only
C. I only
D. II and III only
E. III only

Answer 1

Answer:

B. I and II only.

Step-by-step explanation:

A person who is 61 inches tall is predicted to weight 104.6 pounds according to the regression model.

$y(61)=-115+3.6(61)=-115+219.6=104.6$

The slope of the linear regression model indicates the rate of change of the predicted variable in function of a unit change in the independent variable. In this case, for each additional inch in height, the predicted weight will increase, on average by 3.6 pounds, as indicated by the slope of this model.

As the slope m=3.6 is positive, the correlation is positive: when the independent variable increases, the predicted variable also increases.

Answer 2

A] Both I and II are correct.

Weight = - 115 + 3.6 (Height)

Here, 115 is the autonomous weight at 0 level of height, it is the intercept.  3.6 is the slope, representing change in weight due to change in height. Slope implies that : For every additional inch of height, the predicted weight will increase, on average by 3.6 pounds.                                                                    So, II is True

At height = 61 inches, weight = - 115 + 3.6 (61) = - 115 + 219.6 = 104.6             So, I is  True

Regression shows cause effect relationship (of height on weight). Correlation shows just co-relationship in direction of variables' movement. Nevertheless, positive regression correlation increases the probability of positive correlation (instead of negative correlation)                                           So, III is false

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