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.

The correct answer is B.

Explanation:

Step 1:

The available regression equation is: Predict height= 0.29 + 0.48 (age).

Here, the predict height is dependent variable and the  age is in-dependent variable.

Intercept = 0.29

Slope      = 0.48

The given regression equation indicates the y on x model and the intercept coefficients of the regression equation is 0.29 and the slope is 0.48.

Step 2:

The height increases, an average, by 0.48 m per year.

Because co-efficient of slope variable indicate the positive sign and we increase 1 year in age then automatically height increased is 0.48 m.

The best interpretation of the slope of the regression line is the height increases, on average, by 0.48 meter each year.

The regression line is also called the line of best fit and it is calculated by statisticians using the least squares method.

The regression line describes the quantitative relationship between the dependent and the independent variables. This is useful in making meaningful extrapolations from the line.

The general form of the regression line is y = b + ax where;

Given the specific regression line

predicted height =  0.29 + 048 (age)

The independent variable is the age of the tree and the dependent variable is the height of the tree.

Given the regression line, it is reasonable to say that the best interpretation of the regression line is that the height increases, on average, by 0.48 meter each year.

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