6. Chemosphere (Vol. 20, 1990) published a study of Vietnam veterans exposed to Agent Orange (and the dioxin 2,3,7,8TCDD). The data stored in TCDD.txt gives the amounts of 2,3,7,8TCDD (measured in parts per trillion) in both blood plasma and fat tissue drawn from each of the 20 veterans studied. One goal of the researchers is to determine the degree of linear association between the level of dioxin found in blood plasma and fat tissue. If a linear association between the two variables can be established, the researchers want to build models to predict (1) the blood plasma level of 2,3,7,8-TCDD from the observed level of 2,3,7,8TCDD in fat tissue and (2) the fat tissue level from the observed blood plasma level. (a) Find the prediction equations for the researchers. Interpret the results. (b) Test the hypothesis that fat tissue level (X) is a useful linear predictor of blood plasma level (y). Use 04 = 0.05. (C) Test the hypothesis that blood plasma level (X) is a useful linear predictor of fat tissue level (y). Use or : 0.05. .Intuitively, why must the results of the tests, parts b and (3, agree? Use R only; no need to use calculator. part (d) only (a) : First, build models to predict (1) the blood plasma level of 2,3,7,8-TCDD from the observed level of 2,3,7,8-TCDD in fat tissue: > T X y Regression abline(Regression) > summary(Regression) Call: Im(formula = y ~ x) Residuals : Min 10 Median Max -3.0561 -1. 8120 0. 1556 0.7673 10.2402 Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) -0.1503 0.8413 -0.179 0.86 X 0.9009 0.0784 11. 491 1.01e-09 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 ' . ' 0.1 ' ' 1 Residual standard error: 2.893 on 18 degrees of freedom Multiple R-squared: 0.88, Adjusted R-squared: 0.8734 F-statistic: 132 on 1 and 18 DF, p-value: 1.01e-09 From the above printout, Beta_h_0=-0.1503, Beta_h_1=0.9009, So I got the prediction equations: y_h = (0.9009)x-0.1503 Beta_h_0: When FAT is 0, the predicted starting PLASMA is -0.1503. Beta_h_1:There is a 0.9009 increased in the mean of the starting PLASMA for every 1 increment in FAT.Second, build models to predict (2) the fat tissue level from the observed blood plasma level: > T X y Regression abline(Regression) > summary(Regression) Call: Im(formula = y ~ x) Residuals : Min 10 Median 30 Max -9.5063 -1. 1397 -0. 3631 1.6754 4.8644 Coefficients: Estimate Std. Error t value Pr(>Itl) (Intercept) 0.96972 0. 84646 1. 146 0. 267 X 0.97683 0. 08501 11. 491 1. 01e-09 *** Signif. codes: 0 '***' 0.001 (**) 0.01 '*' 0.05 '. ' 0.1 ' ' 1 Residual standard error: 3.012 on 18 degrees of freedom Multiple R-squared: 0.88, Adjusted R-squared: 0.8734 F-statistic: 132 on 1 and 18 DF, p-value: 1.01e-09 From the above printout, Beta_h_0=0.96972, Beta_h_1=0.97683. So I got the prediction equations: y_h = 0.97683x+0.96972 Beta_h_0: When PLASMA is 0, the predicted starting FAT is 0.96972. Beta_h_1:There is a 0.97683 increased in the mean of the starting FAT for every 1 increment in PLASMA