3. O 01 points | Previcus Notes Ask Your T Consider the accompanying data on x r

Question

3. O 01 points | Previcus Notes Ask Your T Consider the accompanying data on x research and eight different industries. expenditure of dollars) and y = growth rate (% per year) for x 2024 5039 906 3571 1157 327 378 191 y 1.90 3.96 2.44 0.88 0.37-090 0.49 1.01 (a) Would a simple linear regression model provide useful informa expenditure? Use a 0.05 level of significance Calculate the test statistic. (Round your answer to two decimal places.) t# 2.1 tion for predicting growth rate from research and development for this test? (Use a statistical computer package to calculate the P-value. Round your answer to three decimal What is the P-value places.) P-value 0.07 What can you conclude? O Reject Ho. We have convincing evidence of a useful linear relationship between growth rate and O Reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and and expenditure development expenditure. O Do not reject Ho. We have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. Do not reject Ho. We do not have convincing evidence of a useful inear relationship between growth rate and research and development expenditure. Use a 90% confidence interval to estimate the average change in growth rate associated with a S1000 increase ia ex your answer to six decimal places.) (b)

Explanation / Answer

SolutionA:

conduct correlationship test in R to check for linear relationship

x <- c(2024,5039,906,3571,1157,327,378,191)
y <- c(1.90,3.96,2.44,0.88,0.37,-0.90,0.49,1.01)
cor.test(x,y)

output:

Pearson's product-moment correlation

data: x and y

t = 2.2856, df = 6, p-value = 0.06232

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:

-0.04324346 0.93661989

sample estimates:

cor

0.6822184

Solutiona:

t=2.29

p=0.062

p>0.05

Do not reject Null hypothesis.

we do not have convincing evidene of a linear relationship between growth rate and resarch and development exenditure

OPTIOND

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