Question

The correlation between x, ( the diameter of the tree), and Y (the tree’s height) is 0.875064.   A coefficient of correlation of 0.875064 indicates a strong correlation between the independent variable and the dependent variable.   In general, if Y tends to increase along with X, there's a positive relationship.

QUESTION: What does this mean in terms of the problem?

   Is it a strong correlation?

is it statistically significant?

Answer 1

A positive correlation of 0.875064, here indicates that there is quite strong correlation between x and y, which means, as the diameter of the tree increases the height of the tree also increases.

In order to determine if it is statistically significant, we will need the sample size to carry out the t test which is given by,

Null hypothesis H₀: ρ = 0
Alternative hypothesis H_A: ρ ≠ 0 or H_A: ρ < 0 or H_A: ρ > 0

Finally we make a decision,

If the P-value is smaller than the significance level α, we reject the null hypothesis in favor of the alternative. We conclude "there is sufficient evidence at the α level to conclude that the correlation is statistically significant."