A statistical program is recommended. A paper gave the following data on n = 11 female black bears. Age (years) Weight (kg) Home-Range Size (km2) 10.5 54 43.0 6.5 40 46.6 28.5 62 57.4 6.5 55 35.7 7.5 56 62.0 6.5 62 33.8 5.5 42 39.7 7.5 40 32.3 11.5 59 57.2 9.5 51 24.3 5.5 50 68.6 (a) Fit a multiple regression model to describe the relationship between y = home-range size and the predictors x1 = age and x2 = weight. (Round your numerical values to four decimal places.) = (b) If appropriate, carry out a model utility test with a significance level of 0.05 to determine if at least one of the predictors age and weight is useful for predicting home range size. State the null and alternative hypotheses. H0: ?1 = ?2 = 1 Ha: at least one of ?1 or ?2 is not 1.H0: At least one of ?1 or ?2 is not 1. Ha: ?1 = ?2 = 1 H0: ?1 = ?2 = 0 Ha: at least one of ?1 or ?2 is not 0.H0: At least one of ?1 or ?2 is not 0. Ha: ?1 = ?2 = 0 Calculate the test statistic. (Round your answer to two decimal places.) F = Use technology or SALT to calculate the P-value. (Round your answer to four decimal places.) P-value = What can you conclude? Fail to reject H0. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ?1 or ?2 is not 1.Reject H0. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ?1 or ?2 is not 0. Fail to reject H0. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ?1 or ?2 is not 0.Reject H0. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ?1 or ?2 is not 1.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A statistical program is recommended.

A paper gave the following data on n = 11 female black bears.

Age (years)	Weight (kg)	Home-Range Size (km²)
10.5	54	43.0
6.5	40	46.6
28.5	62	57.4
6.5	55	35.7
7.5	56	62.0
6.5	62	33.8
5.5	42	39.7
7.5	40	32.3
11.5	59	57.2
9.5	51	24.3
5.5	50	68.6

(a)

Fit a multiple regression model to describe the relationship between y = home-range size and the predictors

x₁ = age

and

x₂ = weight.

(Round your numerical values to four decimal places.)

(b)

If appropriate, carry out a model utility test with a significance level of 0.05 to determine if at least one of the predictors age and weight is useful for predicting home range size.

State the null and alternative hypotheses.

H₀: ?₁ = ?₂ = 1
H_a: at least one of ?₁ or ?₂ is not 1.H₀: At least one of ?₁ or ?₂ is not 1.
H_a: ?₁ = ?₂ = 1 H₀: ?₁ = ?₂ = 0
H_a: at least one of ?₁ or ?₂ is not 0.H₀: At least one of ?₁ or ?₂ is not 0.
H_a: ?₁ = ?₂ = 0

Calculate the test statistic. (Round your answer to two decimal places.)

F =

Use technology or SALT to calculate the P-value. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Fail to reject H₀. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ?₁ or ?₂ is not 1.Reject H₀. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ?₁ or ?₂ is not 0. Fail to reject H₀. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that at least one of ?₁ or ?₂ is not 0.Reject H₀. We have convincing evidence that the multiple regression model is useful and can conclude that at least one of ?₁ or ?₂ is not 1.

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