Radius and what-not

Question

Data was collected from a sample of 35 trees with diameters between 6 and 48 inches. A regression analysis was run to determine if there is a relationship between the diameter of a tree (x, in inches) and the tree’s age (y, in years). The results of the regression are given below.

y=ax+b
a=6.301
b=-1.044
r2=0.940
r=-0.970

(a) Based on the value given for r, comment on the strength of the linear relationship between diameter and age. Write a complete sentence.

(b) Predict the age of a tree whose diameter is 10 inches and classify this prediction as an interpolation or extrapolation.

Answer 1

Hi Chance,

 

The regression equation is given as y = 6.301x - 1.044 using the values of a and b provided.

y is the age of the tree in years

x is the diameter of the tree in inches 

 

(a) Since r²  is 0.94 we can say that the there is a strong relationship between the age and the diameter of the tree

(because closer the value of r² to 1 , stronger the relationship ) 

we can also say that 94% of the variation in the age of the tree is explained by the variation in diameter. 

 

Value of r =0.97 implies a strong negative linear relationship. 

( negative because the sign of r is -ve)

 

(b) To find the age of a tree whose diameter is 10 in we need to plug in x = 10 in the equation 

so y = 6.301 * 10 - 1.044 = 61.966

Hence age of the tree with diameter 10 in is 61.966 years.

 

This prediction is an intrapolation as we are estimating for diameter = 10 inches which is within the range of diameter of study.

(because it is given that regression is based on trees with diamter between 6 and 48 inches)