Question

An agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine. A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample. Based on the recorded data, the agriculturalist created the following regression equation to predict the height, in meters, of the Australian pine based on the age, in years, of the tree.

predicted height 0.29+048 (age)

Which of the following is the best interpretation of the slope of the regression line?
(A)The height increases, on average, by 1 meter each 0.48 year.
(B)The height increases, on average, by 0.48 meter each year.
(C)The height increases, on average, by 0.29 meter each year.
(D)The height increases, on average, by 0.29 meter each 0.48 year.
(E) The difference between the actual height and the predicted height is, on average, 0.48 meter for each year.

Answer 1

A) The height increases, on average, by 1 meter each 0.48 year.

Explanation:

Given that an agriculturalist working with Australian pine trees wanted to investigate the relationship between the age and the height of the Australian pine.

A random sample of Australian pine trees was selected, and the age, in years, and the height, in meters, was recorded for each tree in the sample

Regression was run and the equation was found to be

`h = 0.29+0.48a`, where a represents age in years and h theheight of the tree.

The slope 0.48 is positive gives the rate of change of height for a unit change in age

Since positive increase in height whenever increase in age

A) The height increases, on average, by 1 meter each 0.48 year.