(10 points) Using data from 1000 hospital patients, the average length of hospital stay

| November 24, 2016

3. (10 points) Using data from 1000 hospital patients, the average length of hospital stay (indays) was modeled as:length = 3.1 + .24 cigarettes – .15 obesity + .86 prescrip – .023 cholesterol (1.5) (.17) (.82) (1.85) (.062)n = 1,000 R2= 0.383 cigarettes: the number of packs of cigarettes smoked per day; obesity: the number of pounds a patient is over the obesity threshold for their age height; prescript: the number of prescription pills taken each day; cholesterol: the patient’s blood cholesterol level.Despite standard errors being high and t-stats being low, an F-test reveals that obesity,prescript, and cholesterol are jointly highly significant. Dropping obesity and cholesterol, theequation is re-estimated as:length = 3.1 + .44 cigarettes + .76 prescrip(1.1) (.21) (.22)n = 1,000 R2= 0.343

a) Calculate the t-statistic on prescrip in the new and old regression.

b) What is the most likely reason that the standard error for prescrip is much lower in thesecond mode

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