Question

Cost-to-charge ratio (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
Hospital	Outpatient Care	Inpatient Care
1	62	80
2	66	76
3	63	75
4	51	62
5	75	100
6	65	88
7	56	64
8	45	50
9	48	54
10	71	83
11	54	100

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

Solution Given that: cast-to-charge Ratio Hospital out pabent In patient care cale 62 80 76 a 66 63 3 75 4 51 62- 100 75 65 88 7 56 64 8 45 50 9 48 54 10 1 83 11 54 100 the g g * An outler is a data point whose e esponre y does not follow general tiend the rest the data A data point is influential if it unduty influences a segaesion analysis such as the predicted responser; the estimated slope coefficients of the hypothesis test tesults. any • part of

In patient OUHICS 100 Influential (54,100) 8.100) 90 ( ก 80 707 60 50 45 55 65 75 la) of the data out patient Hospital 5: (75,100) Hospital 11: [54,100] No, the observations dosee vation, because the point whose response 'y' does not follow jos hospital II is not an influenkal the general teend the rest b. yes, the obscercition for hospital II is an outlice because the point whose lesponse Sy does not follow the general teend g the sest the data yes, the observation fos hospital 5. is an influential observation, follows general teend to be from the rest of the data in the direction the observation dos hospital 5 is not an outlice because feend the rest certainly appears to be far data in the x-direction. g the it because the eest of of the data and certainly appears jas lemoved X- id, NO, it follows the general g lemoved of the data from the rest of the