Consider the accompanying data on x = research and development expenditure (millions of dollars) and y= growth rate (% per year) for eight different industries. X 2.023 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 -0.9 0.49 1.01 LUSE SALT (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 = 0.98 ]x Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value= What can you conclude? O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Ⓒ Fail to reject H. 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 or the Distribution Calculators page in SALT to find the critical value. Round your answers to four decimal places.) 0.1029 % per yr Interpret the resulting interval. O 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. O 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. O 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.
Consider the accompanying data on x = research and development expenditure (millions of dollars) and y= growth rate (% per year) for eight different industries. X 2.023 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 -0.9 0.49 1.01 LUSE SALT (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 = 0.98 ]x Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value= What can you conclude? O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Ⓒ Fail to reject H. 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 or the Distribution Calculators page in SALT to find the critical value. Round your answers to four decimal places.) 0.1029 % per yr Interpret the resulting interval. O 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. O 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. O 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.
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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![Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries.
X 2.023 5.039 0.906 3.573 1.157 0.327 0.378
y
1.90 3.96 2.44
USE SALT
0.88
0.37
0.191
-0.9 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 = 0.98
x
Use technology to find the P-value for this test. (Round your answer to four decimal places.)
P-value=
What can you conclude?
O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
O Reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
O Fail to reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
Ⓒ Fail to reject H.. 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 or the Distribution Calculators page in SALT to find the critical value. Round your answers to four decimal places.)
0.1029
]) % per yr
Interpret the resulting interval.
O 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.
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.
O 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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d0d4d96-9793-47e3-bc41-3d25b50aa5a7%2F538bdf7e-b3b7-4be6-a5fa-b8b0cb719f6f%2F725ptp_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the accompanying data on x = research and development expenditure (millions of dollars) and y = growth rate (% per year) for eight different industries.
X 2.023 5.039 0.906 3.573 1.157 0.327 0.378
y
1.90 3.96 2.44
USE SALT
0.88
0.37
0.191
-0.9 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 = 0.98
x
Use technology to find the P-value for this test. (Round your answer to four decimal places.)
P-value=
What can you conclude?
O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
O Reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
O Fail to reject H. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure.
Ⓒ Fail to reject H.. 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 or the Distribution Calculators page in SALT to find the critical value. Round your answers to four decimal places.)
0.1029
]) % per yr
Interpret the resulting interval.
O 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.
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.
O 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.
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