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 2.025 5.039 0.904 3.573 1.157 0.327 0.378 0.191 y 1.90 3.96 USE SALT 2.44 0.88 0.37 -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 = 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 Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between growth rate and research and development expenditure. O Fail to reject H. We have…

3. A study of beer consumption using the annual data from 1980 -2001 produced the following regression: Y = 0.41 +0.052.X₁; −0.047X2; +0.032X3; −0.018X4i (0.027) (0.011) (0.009) (0.008) (0.009) R² = 0.94 F = 66.58 DW statistic=1.32, figures in the brackets are standard errors Where: Y₁ = Annual aggregate beer consumption in year t (billion pints) X₁₁ = Real disposable income income in year t ($ billions at 2001 prices) X2i = Price of beer in year t (index number with 2001 = 100) X31 Price of wine and sprits in year t (index number with 2001 = 100) = X4₁ = Price of cigarettes in year t (index number 2001 = 100) (a) What is the effect of a change in the price of beer on beer consumption? Does it have the correct sign? Explain. (b) Comment on the signs of the other three coefficients. Are they as expected? (c) Tests the significance of the coefficients on each of the variables Xit i = 1, 2, 3, 4. What assumptions have you made in carrying out these tests? (d) What conclusion do you draw…

19

The table below shows (lifetime) peptic ulcer rates (per 100 population), UU, for various family incomes, xx, as reported by the 1989 National Health Interview Survey.   Income 4000 6000 8000 12000 16000 20000 30000 45000 60000 Ulcer rate 14.1 13.1 13.8 12.6 11.8 11.7 11.5 9.3 7.6 (a) Find the equation of the regression line. Ulcer rate, U(x)=  . (b) Estimate the peptic ulcer rate for an income level of x0= 25000 according to the linear model in part (a). Ulcer rate, U(x0)=  .

The accompanying scatterplot shows the relationship between the age of an internet user and the amount of time spent browsing the internet per week​ (in minutes). The accompanying residual plot is also shown along with the QQ plot of the residuals. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. Choose the statement that best describes whether the condition for Normality of errors does or does not hold for the linear regression model. A.The residual plot displays a fan​ shape; therefore the Normality condition is not satisfied.B.The QQ plot mostly follows a straight​ line; therefore the Normality condition is satisfied.C.The scatterplot shows a negative​ trend; therefore the Normality condition is satisfied.D.The residual plot shows no​ trend; therefore the Normality condition is not satisfied.

A simple linear regression model was created to examine the relationship between the age of patients in years (i.e. the independent variable) and the patients' scores on a questionnaire that measures quality of life (i.e. the dependent variable). There were n=20 patients in the study, and some of the results of the regression are presented below: Estimated slope = -0.64 Standard error of the slope = 0.52 Estimated intercept = 42.0 Standard error of the intercept = 13.6 Based on these results, what would be the expected quality of life score for a patient who is 30 years old?   Question 3 options:   61.2   22.8   1260.64   29.2