Question

A regression was run to determine whether 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. Use this to predict the age of a tree with diameter 10 inches.y=ax+ba=6.301b=-1.044r=-0.970Using the information above, we can conclude that a tree with a diameter of 10 inches will be Answer years old. Type your answer rounded to the nearest hundredth.The r value indicates a Answer

Answer 1

$\begin{gathered} \text{Given} \\ a=6.301 \\ b=-1.044 \\ r=-0.970 \end{gathered}$

Using the given above, we can model the equation as

$y=6.301x-1.044$

If the tree has a diameter of 10 inches (x), then we can solve how old it is by

$\begin{gathered} y=6.301x-1.044 \\ y=6.301(10)-1.044=6301-1.044 \\ y=61.966 \\ \text{Rounded to the nearest hundredth} \\ y=61.97 \end{gathered}$

Therefore, we can conclude that a tree with a diameter of 10 inches will be 61.97 years old.

The r value is -0.970. Judging by the sign, we can infer that the correlation is negative.

The value is also very very close to -1, which implies a perfect correlation.

We can say therefore that the r value indicates a strong negative correlation.