A geospatial scientist was mapping Virginia White Pines in a nearby national forest. He collected data on:

tree species
tree height (meters)
tree circumference at breast height (centimeters)
tree age (in years)
Number of drought years in the tree's lifetime

The correlation coefficient is
𝑟
=
−
0.98
. What does this indicate about the relationship between drought years and tree circumference?

Question

A geospatial scientist was mapping Virginia White Pines in a nearby national forest. He collected data on:

tree species
tree height (meters)
tree circumference at breast height (centimeters)
tree age (in years)
Number of drought years in the tree's lifetime

The correlation coefficient is  
𝑟
=
−
0.98
. What does this indicate about the relationship between drought years and tree circumference?

BlackTom AI · Accepted Answer

A correlation coefficient of r = −0.98 indicates a very strong negative linear association between the two measured variables.

1) Relevant concepts:
- The Pearson correlation coefficient r ranges from −1 to +1. Its sign shows the direction (negative means as one variable increases, the other tends to decrease). Its magnitude (absolute value) measures strength: values near 1 indicate a very strong linear relationship, values near 0 indicate little or no linear relationship.
- r^2 (the coefficient of determination) gives the proportion of variance in one variable explained by a linear relationship with the other.

2) Step-by-step reasoning:
- Given r = −0.98, the sign is negative, so the relationship is inverse: more drought years correspond to smaller tree circumferences.
- The magnitude |r| = 0.98 is very close to 1, indicating the relationship is nearly perfectly linear.

3) Calculations (intermediate steps):
- Compute r^2 = (−0.98)^2 = 0.9604.
- Interpret r^2: about 0.9604 × 100% = 96.04% of the variance in tree circumference can be linearly associated with the number of drought years (in this sample), assuming linear model conditions.

4) Why the correct answer is correct:
- The negative sign gives the direction (negative relationship) and the magnitude near 1 gives strong strength; together this precisely describes a strong negative linear relationship between drought years and circumference.

5) Why other possible interpretations are incorrect:
- “Strong positive” would contradict the negative sign.
- “Weak relationship” contradicts the magnitude being near 1.
- “No relationship” is wrong because r is far from zero.
- “Nonlinear relationship” is unlikely given such a high |r| for the Pearson measure; a strong linear fit is indicated.

Conclusion: Therefore the best description is “A strong negative linear relationship,” which matches the provided correct answer.

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