Blackeared wheatears are small birds of Spain and Morocco. Males of the species demonstrate an exaggerated sexual display by carrying many heavy stones to nesting cavities. This 35-gram bird transports, on average, 3.1 kg of stones per nesting season! Different males carry somewhat different sized stones, prompting a study of whether larger stones may be a signal of higher heaEth status. M. Soler et al. calculated the average stone mass (g) carried by each of 21 male blackeared wheatears, along with Tcell response measurements (in mm) reflecting their immune system strengths. Analyze the data and write a statistical report (by answering the questions below); treat the Tcell as the response and the stone mass as the explanatory variable. You may assume all criteria for regression and related ttests are met. You can find the data for this problem on 2DS. (Male Display Data Set) Analyze the data, providing the following: a. Provide a scatterplot with 99% confidence intervals of the regression line and 99% prediction intervals ofthe regression line. Please do this in R. b. Provide a table showing the tstatistics and pvalues for the significance of the regression parameters BOA l (as different from 0). Please do this in R. c. Using the output in (b), show all 6 steps of each hypothesis test. (That's one test for B =0 31:0 o and one test for .) Find critical values in R. Your conclusion should include a confidence interval .Use alpha = 0.01. d. State the regression equation. Be careful to use the mean Tcell or predicted Tcell, rather than just Tcell. e. Interpret the slope in the model (regression equation). f. Interpret the yintercept in the model (regression equation). g. Find and interpret the 99% confidence interval for the mean tcell response conditional on a stone mass of4.5 grams. Please do this directly in R. h. Find and interpret the 99% prediction interval for the predicted tcell response given a stone mass of 4.5 grams. Please do this directly in R. i. Calibrationintervals: 1. Using the graphicalmethod (using your bestjudgment using the graphs from part (a)), find the following using R, as part (a) was done in R. a. 99% calibration interval for the mean tcell response of0.3. b. 99% calibration interval for a single tcell response of0.3. 2. Using software directly, find the following using R, as SAS does not provide calibration intervals directly. (R: package investr) a. 99% calibration interval for the mean t-cell response of0.3. b. 99% calibration interval for a single t-cell response of0.3. 3. Interpret the following using the results from (1) and (2) above. a. 99% calibration interval for the mean tcell response of0.3. b. 99% calibration interval for a single tcell response of0.3. j. Provide a scatterplot of residuals. Please do this in R. k. Provide a histogram of residuals with a normal distribution superimposed. It might be helpful to use studentized residuals, rather than regular residuais, with a normal curve
