Question

Measuring the height of a tree is usually more difficult than measuring the diameter of the tree. Therefore, many researchers use regression models to predict the height of a tree from its diameter measured at 4 feet 6 inches from the ground. The following computer output shows the results of a linear regression based on the heights, in feet, and the diameters, in inches, recorded from 31 felled trees.
Estimate Std Error t-value Pr(>|t|)

Intercept 62. 031 4. 383 14. 15 0. 0000

Diameter 1. 054 0. 322 0. 2028 3. 27


Required:

What is a 95 percent confidence interval for the slope of the population regression line?

Answer 1

Measuring the height of a tree is usually more difficult than measuring the diameter of the tree, confidence interval for the slope is mathematically given as

C=(0.396, 1.712)

What is a 95 percent confidence interval for the slope of the population regression line?

Generally, the equation for the confidence interval  is mathematically given as

$C=\beta-tn-2, \alpha /2 (S.E)$

Where

$\beta=1.054$

Therefore

C=(1.054-t29, 0.025*0.322)

C=(0.396, 1.712)

In conclusion, the  95 percent confidence interval is

C=(0.396, 1.712)

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