Question

Suppose that an arborist wishes to see if there is a relationship between the heights of baobabs in Madagascar forests and their diameters. He selects 10 baobabs at random from the forest and measures their heights and diameters. To ensure consistent measurements, he records the diameters around the tree from a height of 1.4 metres above the ground.

Determine the equation of the linear regression line.

1. Determine the equation of the linear regression line.
2. Test for association using the Spearman rank correlation. Be sure to carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.
3. Test for linear association using Pearson’s correlation coefficient. Be sure to carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.
4. Test for significance using Kendall’s tau. Perform the test by hand using a normal approximation to determine the p-value. Carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.

Data given below:

Diameter (m)	Height (m)
26	29.6
24.1	27.8
11.5	16.8
12.8	15.6
19.3	28.5
16.4	15.3
18	28.2
14.9	23
11.2	10.7
13.9	22.9

Answer 1

a)

b) Test for association using the Spearman rank correlation. Be sure to carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.

Ans:

Spearman rank correlation test using R software

The p-value for the test is 0.0002302 and less than 0.05 level of significance. Hence, we can conclude that there is a statistically association between the Diameter (m) and Height (m).

c) Test for linear association using Pearson’s correlation coefficient. Be sure to carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.

Ans:

The p-value for the test is 0.000 and less than 0.05 level of significance. Hence, we can conclude that there is a statistically association between the Diameter (m) and Height (m).

d) Test for significance using Kendall’s tau. Perform the test by hand using a normal approximation to determine the p-value. Carefully state your null and alternative hypothesis, and conduct the test at the 0.05 significance level.

Ans:

The p-value for the test is 0.0003666 and less than 0.05 level of significance. Hence, we can conclude that there is a statistically association between the Diameter (m) and Height (m).

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