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.

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	5.039	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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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