consider the accompanying data X=research and development expenditure thousands of dollars and Y=growth rate % per year for eight different industries.

X 2022 5040 907 3574 1157 327 378 191

Y 1.90 3.96 2.44 0.88 0.37 -0.90 1.49 1.01

a. would a simple linear regression model provide useful information for predicting growth rate from research and development expenditure? use a 0.05 level of confidence.

state the appropriate null and alternative hypothesis.

calculate the test statistic and P value for this test.

state the conclusion in the problem context.

b. use a 90% confidence interval to estimate the average change in growth rate in % per year associated with a $1000 increase in expenditure.

interpret the resulting interval.