Question

Cost-to-charge ratlo (the percentage of the amount billed that represents the actual cost) for Inpatient and outpatient services at 11 Oregon hospitals is shown in the following table. A scatterplot of the data is also shown. Cost-to-Charge Ratio Outpatient Inpatient Hospital Care Care 1 62 80 2 66 76 3 63 75 4 51 62 5 75 100 88 6 65 7 56 64 8 45 50 9 48 54 10 71 83 11 54 100 Inpatient 100 90 80 70 60 50 45 55 65 75 Outpatient

The least-squares regression line with y = inpatient cost-to-charge ratio and x = outpatient cost-to-charge ratio is  = -1.1 + 1.29 x.

(a) Is the observation for Hospital 11 an influential observation?

YesNo    

(b) Is the observation for Hospital 11 an outlier?

YesNo    

(c) Is the observation for Hospital 5 an influential observation?

YesNo    

(d) Is the observation for Hospital 5 an outlier?

YesNo    

Answer 1

1 D Given that the last square regression equation is 9 =-1.1+1.29x Whers û = Inpatienly cost to changye ratio x - outpatients The prediçded valuesby, w first computed by substituting each value of x in the equation of least soprati square. The residural are then obtained by substreeting Ý from y The value of r2 is then computed using given formula, r21 wherry {cy-?,? Ily-y)? Here, r2 in the given equution, SS Res SST ssresa SST = r = 0.5329 Now, no remove istospital 11 dada then our pa least square regresion equation, û =-17.589+ 1.5081% and r2 = 0.9124 a so increening the r2 value. soma) The observation for Hospitel 14 an infiluential point. (yes) b) The observation for Hospital 11 an oublier (yes) Now remove Hospital s data, then the con least square regression ŷ: 5-26 28+ 1.169376 and r² = 0.4093 , so, R² decreases. e) The observation for Hospital 5 an influential point (NO) d) The observation for Hospital 5 an outlier.(No). equation CScared with me