A statistical program is recommended. The authors of an article found that the speed of a prey (twips/s) and the length of a prey (twips ✕ 100) are good predictors of the time (seconds) required to catch the prey. (A twip is a measure of distance used by programmers.) Data were collected in an experiment in which subjects were asked to "catch" an animal of prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which the prey moved across the screen. The following data are consistent with summary values and a graph given in the article. Each value represents the average catch time over all subjects. The order of the various speed-length combinations was randomized for each subject. Prey Length Prey Speed Catch Time 7 20 1.11 6 20 1.21 5 20 1.22 4 20 1.41 3 20 1.51 3 40 1.39 4 40 1.37 6 40 1.30 7 40 1.28 7 80 1.41 6 60 1.38 5 80 1.39 7 100 1.43 6 100 1.42 7 120 1.70 5 80 1.49 3 80 1.40 6 100 1.50 3 120 1.90 (a) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. (Use x1 for prey length and x2 for speed. Round your numerical values to three decimal places.) = (b) Predict the catch time for an animal of prey whose length is 6 and whose speed is 50. (Round your answer to three decimal places.) s (c) Is the multiple regression model useful for predicting catch time? Test the relevant hypotheses using ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: neither ?1 nor ?2 is 0.H0: at least one of ?1 or ?2 is not 0. Ha: ?1 = ?2 = 0 H0: ?1 = ?2 = 0 Ha: at least one of ?1 or ?2 is not 0.H0: neither ?1 nor ?2 is 0. Ha: ?1 = ?2 = 0 Calculate the test statistic. (Round your answer to two decimal places.) F = Use technology 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 0.Reject H0. We have convincing evidence that the multiple regression model is useful and can conclude that neither ?1 nor ?2 is 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 0.Fail to reject H0. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that ?1 and ?2 are both not 0. (d) The authors of the article suggest that a simple linear regression model with the single predictor x = length speed might be a better model for predicting catch time. Calculate these x values and use them to fit a simple linear regression model. (Round your numerical values to three decimal places.)

A statistical program is recommended. The authors of an article found that the speed of a prey (twips/s) and the length of a prey (twips ✕ 100) are good predictors of the time (seconds) required to catch the prey. (A twip is a measure of distance used by programmers.) Data were collected in an experiment in which subjects were asked to "catch" an animal of prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which the prey moved across the screen. The following data are consistent with summary values and a graph given in the article. Each value represents the average catch time over all subjects. The order of the various speed-length combinations was randomized for each subject. Prey Length Prey Speed Catch Time 7 20 1.11 6 20 1.21 5 20 1.22 4 20 1.41 3 20 1.51 3 40 1.39 4 40 1.37 6 40 1.30 7 40 1.28 7 80 1.41 6 60 1.38 5 80 1.39 7 100 1.43 6 100 1.42 7 120 1.70 5 80 1.49 3 80 1.40 6 100 1.50 3 120 1.90 (a) Fit a multiple regression model for predicting catch time using prey length and speed as predictors. (Use x1 for prey length and x2 for speed. Round your numerical values to three decimal places.) = (b) Predict the catch time for an animal of prey whose length is 6 and whose speed is 50. (Round your answer to three decimal places.) s (c) Is the multiple regression model useful for predicting catch time? Test the relevant hypotheses using ? = 0.05. State the null and alternative hypotheses. H0: ?1 = ?2 = 0 Ha: neither ?1 nor ?2 is 0.H0: at least one of ?1 or ?2 is not 0. Ha: ?1 = ?2 = 0 H0: ?1 = ?2 = 0 Ha: at least one of ?1 or ?2 is not 0.H0: neither ?1 nor ?2 is 0. Ha: ?1 = ?2 = 0 Calculate the test statistic. (Round your answer to two decimal places.) F = Use technology 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 0.Reject H0. We have convincing evidence that the multiple regression model is useful and can conclude that neither ?1 nor ?2 is 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 0.Fail to reject H0. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that ?1 and ?2 are both not 0. (d) The authors of the article suggest that a simple linear regression model with the single predictor x = length speed might be a better model for predicting catch time. Calculate these x values and use them to fit a simple linear regression model. (Round your numerical values to three decimal places.)

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.

The authors of an article found that the speed of a prey (twips/s) and the length of a prey (twips ✕ 100) are good predictors of the time (seconds) required to catch the prey. (A twip is a measure of distance used by programmers.) Data were collected in an experiment in which subjects were asked to "catch" an animal of prey moving across his or her computer screen by clicking on it with the mouse. The investigators varied the length of the prey and the speed with which the prey moved across the screen.

The following data are consistent with summary values and a graph given in the article. Each value represents the average catch time over all subjects. The order of the various speed-length combinations was randomized for each subject.

Prey Length	Prey Speed	Catch Time
7	20	1.11
6	20	1.21
5	20	1.22
4	20	1.41
3	20	1.51
3	40	1.39
4	40	1.37
6	40	1.30
7	40	1.28
7	80	1.41
6	60	1.38
5	80	1.39
7	100	1.43
6	100	1.42
7	120	1.70
5	80	1.49
3	80	1.40
6	100	1.50
3	120	1.90

(a)

Fit a multiple regression model for predicting catch time using prey length and speed as predictors. (Use x₁ for prey length and x₂ for speed. Round your numerical values to three decimal places.)

(b)

Predict the catch time for an animal of prey whose length is 6 and whose speed is 50. (Round your answer to three decimal places.)

(c)

Is the multiple regression model useful for predicting catch time? Test the relevant hypotheses using ? = 0.05.

State the null and alternative hypotheses.

H₀: ?₁ = ?₂ = 0
H_a: neither ?₁ nor ?₂ is 0.H₀: at least one of ?₁ or ?₂ is not 0.
H_a: ?₁ = ?₂ = 0 H₀: ?₁ = ?₂ = 0
H_a: at least one of ?₁ or ?₂ is not 0.H₀: neither ?₁ nor ?₂ is 0.
H_a: ?₁ = ?₂ = 0

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

F =

Use technology 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 0.Reject H₀. We have convincing evidence that the multiple regression model is useful and can conclude that neither ?₁ nor ?₂ is 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 0.Fail to reject H₀. We do not have convincing evidence that the multiple regression model is useful and cannot conclude that ?₁ and ?₂ are both not 0.

(d)

The authors of the article suggest that a simple linear regression model with the single predictor

x =

length

speed

might be a better model for predicting catch time. Calculate these x values and use them to fit a simple linear regression model. (Round your numerical values to three decimal places.)

(e)

Which of the two models considered (the multiple regression model from part (a) or the simple linear regression model from part (d)) would you recommend for predicting catch time? Justify your choice.

Since the r² value is greater for the second model than for the first, but the adjusted r² value is greater for the first model than for the second, the first model is preferable to the second. The first model is the one that accounts for the greater proportion of the observed variation in catch time.Since both the r² and the adjusted r² values are greater for the first model than for the second, the first model is preferable to the second. The first model is the one that accounts for the greater proportion of the observed variation in catch time. Since the r² value is greater for the first model than for the second, but the adjusted r² value is greater for the second model than for the first, the second model is preferable to the second. The second model is the one that accounts for the greater proportion of the observed variation in catch time.Since both the r² and the adjusted r² values are greater for the second model than for the first, the second model is preferable to the first. The second model is the one that accounts for the greater proportion of the observed variation in catch time.

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