Measuring tree height is not an easy task. How well might trunk diameter predict

Question

Measuring tree height is not an easy task. How well might trunk diameter predict tree height? A survey of 958 live trees in an old-growth forest in Canada answered this question. Here is part of the computer output based on these data for regressing height on diameter, both in centimeters (cm), along with prediction for a tree having a diameter of 50 cm:

0.0000

S=67427 R-Sq=92.5% R-Sq(adj)=92.5%

New

Obs Fit SE Fit 95% CI    95% PI

1 30.217 0.179    (29.865, 30.569)    (22.997, 37.436)

(a) A scatterplot of the data shows a reasonably linear relationship between tree height and diameter. Is this relationship statistically significant? How strong is the relationship?

(b) Give a 95% confidence interval for the height of 1 tree randomly selected from this forest if the tree has a diameter of 50 cm.

(c) Now give a 95% confidence interval for the mean height of all the trees in this forest that have a diameter of 50 cm. How does this interval compare with the one you calculated in (b)?

predictor Coef SE Coef T P Constant 2.6696 0.1677 15.92 0.0000 Diameter 0.550940 0.005058 108.93

0.0000

Explanation / Answer

The r2 value is 0.925

the correlation coefficient is

r2 = sqrt(0.925)
= 0.9617

as the p value is less than 0.05 , hence the result is signficant

b)

The 95% Ci is given as

Obs Fit SE Fit 95% CI 95% PI
1 30.217 0.179 (29.865, 30.569) (22.997, 37.436)

the 95% CI (29.865, 30.569)

c)

we cannot answer this without the data

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

---