Answered

IDNLearn.com is the perfect place to get detailed and accurate answers to your questions. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

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 0.0028 3.27
Which of the following is a 95 percent confidence interval for the slope of the population regression line?
(A) (0.001.2.107).
(B) (0.396, 1.712.
(C) (0.423,1.685).
(D) (0.732. 1.376).
(E) (53.07.70.99).

Sagot :

Ajeigbeibraheemidn

Answer:

(B) (0.396, 1.712)

Step-by-step explanation:

From the information given;

Confidence Interval = 0.95

Significance Level [tex]= 1 - 0.95 = 0.05[/tex]

The confidence interval for regression coefficient beta (whereby in this case it is the coefficient of the diameter) is expressed by:

= [tex]( Beta ^- \ t_{n-2}, \alpha/2 ( S.E \ of \ \^ \ \ ), Beta^+ \ t_{n-2}, \alpha/2 ( S.E \ of \ \^ \ \ ))[/tex]

From the regression coefficient, the estimated value of beta^  = 1.054

[tex]= (1.054 - t_{29,0.025} *(0.322), 1.054 + t_{29,0.025}*(0.322))[/tex]

[tex]t_{229,0.025} = 2.0452\\\\ = \mathbf{(0.396, 1.712)}[/tex]

Your presence in our community is highly appreciated. Keep sharing your insights and solutions. Together, we can build a rich and valuable knowledge resource for everyone. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.