2. Question Details The extent of disease transmission can be affected greatly by the viability of infectious organisms suspended in the air. Because of the infectious nature of the disease under study, the viability of these organisms must be studied in an airtight chamber. One way to do this is to disperse an aerosol cloud, prepared from a solution containing the organisms, into the chamber. The biological recovery at any particular time is the percentage of the total number of organisms suspended in the aerosol that are viable. The data in the accompanying table are the biological recovery percentages computed from 13 different aerosol clouds. For each of the clouds, recovery percentages were determined at different times. Download the related data (.xls format) and run JMP to answer the following questions. i. Look at the scatter plot of the data. Do you observe a linear relationship? yes no Compute the log of the biological recovery. Look at the scatter plot for the time (x) versus log of the biological recovery. Do you observe a better linear relationship? no yes ii. Fit the linear regression model y=beta0+beta1*x+epsilon where y is the log of the biological recovery. What is the estimated mean of y at 0 minute? What is the estimated mean change in y for the 1 minute increase in x? What is the estimated error variance in the model? What is the estimated percent variability in y explained by the model linear relationship with x? % iii. Does y appear to be in a constant increasing relation with x? no as we failed to reject H0 when testing the slope and estimated slope is negative no as we rejected H0 when testing the slope and estimated slope is negative yes as we rejected H0 when testing the slope and estimated slope is positive yes as we failed to reject H0 when testing the slope and estimated slope is negative iv. Estimate the mean log biological recovery percentage at 30 minutes. Obtain the 99% confidence interval for the mean log biological recovery percentage at 30 minutes, lower upper v. What is the use of a hat values in a linear regression? to find influential points to check if the residuals has mean zero to check if the response follows a normal distribution to find maximum error variance to check if the homoscadasticity assumption is satisfied Cloud Time 1 2 3 4 5 6 7 8 9 10 11 12 13 0 5 10 15 20 25 30 35 40 45 50 55 60 Recover% 70.6 52 33.4 22 18.3 15.1 13 10 9.1 8.3 7.9 7.7 7.7