(a) Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Fail to reject H0. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Fail to reject H0. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Reject H0. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. (b) Use a 90% confidence interval to estimate the average change in growth rate associated with a $1,000,000 increase in expenditure. (Use technology to find the critical value. Round your answers to four decimal places.) ( , ) % per yr

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

Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries.

x	2.025	5.037	0.906	3.573	1.157	0.327	0.378	0.191
y	1.90	3.96	2.44	0.88	0.37	−0.90	0.49	1.01

(a)

Would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? Test the appropriate hypotheses using a 0.05 significance level.

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

t =

Use technology to find the P-value for this test. (Round your answer to four decimal places.)

P-value =

What can you conclude?

Reject H₀. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.

Fail to reject H₀. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.

Fail to reject H₀. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.

Reject H₀. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.

(b)

Use a 90% confidence interval to estimate the average change in growth rate associated with a $1,000,000 increase in expenditure. (Use technology to find the critical value. Round your answers to four decimal places.)

( , ) % per yr

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