10 points Using data from 1000 hospital patients the averag

. (10 points) Using data from 1000 hospital patients, the average length of hospital stay (in days) 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, the equation 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 the second model?

Solution