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 5.039 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 Interpret the resulting interval. We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is outside this interval.We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is in this interval. We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is outside this interval.We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is in this interval.

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 5.039 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 Interpret the resulting interval. We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is outside this interval.We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is in this interval. We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is outside this interval.We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is in this interval.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

See similar textbooks

Related questions

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	5.039	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

Interpret the resulting interval.

We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is outside this interval.We are 90% confident that the mean change in growth rate associated with a $1,000 increase in research and development expenditure is in this interval. We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is outside this interval.We are 90% confident that the mean change in research and development expenditure associated with a 1 percent change in growth rate is in this interval.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here