Biostatistics_21. A study examined predictors of high-density lipoprotein (HDL), the so-called good cholesterol (measured in mg/dl with a range of XXXXXXXXXXOne early model had the following...

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Biostatistics_2 1. A study examined predictors of high-density lipoprotein (HDL), the so-called good cholesterol (measured in mg/dl with a range of 14-130). One early model had the following output (note that drinkany = 1 if the subject drank any alcohol on a weekly basis, 0 for non- drinkers or drinkers less than once per week): a) What kind of model is shown here? b) Relate the ANOVA table with the R-squared value. c) What does the TSS represent? d) How is the constant interpreted in this model? e) For someone who drinks, what is their predicted HDL? f) True or false and why: Since the p-value is so small, we know that the coding of drinkany described in the narrative was a very good way to measure alcohol consumption. g) Here is a plot of the standardized residuals. What is the purpose of this plot? What should the shape and mean value of the residuals be? Why is it important that the mean value be what you say it should? _cons 48.54985 .3183238 152.52 0.000 47.92567 49.17403 drinkany 4.346893 .509133 8.54 0.000 3.348571 5.345216 HDL Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 478784.373 2749 174.166742 Root MSE = 13.028 Adj R-squared = 0.0255 Residual 466412.126 2748 169.727848 R-squared = 0.0258 Model 12372.2467 1 12372.2467 Prob > F = 0.0000 F( 1, 2748) = 72.89 Source SS df MS Number of obs = 2750 0 10 0 20 0 30 0 40 0 Fr eq ue nc y -2 0 2 4 6 Standardized residuals The variable age (in years, 44-79) was added to the above model to produce this output: h) Briefly discuss if adding age improves the model or not (1-2 sentences is enough). i) What is the predicted HDL for a 72 year old subject who drinks alcohol? j) Does it appear that age substantially confounds the drinkany --> HDL relationship? Why or why not? The variable triglyceride level (tri, in mg/ml) was added next. k) Which of the two variables that were already in the model does triglycerides confound the most? l) How much of the variability of hdlc is explained by the new model? This diagnostic was produced: _cons 31.91285 2.504818 12.74 0.000 27.00133 36.82436 drinkany 4.530639 .5058657 8.96 0.000 3.538723 5.522554 age .2485771 .0371264 6.70 0.000 .1757787 .3213755 HDL Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 478784.373 2749 174.166742 Root MSE = 12.925 Adj R-squared = 0.0408 Residual 458922.872 2747 167.063295 R-squared = 0.0415 Model 19861.5007 2 9930.75035 Prob > F = 0.0000 F( 2, 2747) = 59.44 Source SS df MS Number of obs = 2750 _cons 46.57759 2.379594 19.57 0.000 41.91161 51.24356 tri -.0825835 .0035811 -23.06 0.000 -.0896054 -.0755616 age .2394362 .0339899 7.04 0.000 .1727879 .3060845 drinkany 3.638736 .4647102 7.83 0.000 2.727519 4.549952 hdlc Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 478784.373 2,749 174.166742 Root MSE = 11.833 Adj R-squared = 0.1961 Residual 384465.011 2,746 140.009108 R-squared = 0.1970 Model 94319.3619 3 31439.7873 Prob > F = 0.0000 F(3, 2746) = 224.56 Source SS df MS Number of obs = 2,750 . regress hdlc drinkany age tri m) Explain whether this is good or bad and what its purpose is. n) A linktest was done and had a hat value of 0.021 and a hatsq value of 0.091. Explain what these values mean. o) What is the purpose of this plot and what do you conclude? 2. In a study that