2. Exercise 14.4 Mental Health Care. Exercise 14.2 introduced historical data in

Question

2. Exercise 14.4 Mental Health Care. Exercise 14.2 introduced historical data in which the explanatory variable was the reciprocal of the distance to the nearest healthcare facility (miles ? 1, variable name REC_DIST) and the response variable was the percent of patients cared for at home (variable name PHOME2). Table 14.6 lists the data. Eliminate observation 13 (Nantucket) and then determine the least square regression coefficients for the data.

TABLE 14.6 Data for Exercise 14.2. Percent of mental healthcare patients cared for in the home (PHOME), distance to the nearest mental healthcare center (DIST; miles), and reciprocal of the distance to the nearest mental healthcare center (REC_DIST; miles-1) PHOME DIST REC DIST 0.01031 0.01613 0.01852 0.01923 0.05000 0.07143 0.10000 0.25000 0.07143 0.07143 0.06250 0.02273 0.01299 0.01923 COUNTY Berkshire Franklin Hampshire Hampden Worcester Middlesex Essex Suffolk Norfolk Bristol Plymouth Barnstable Nantucket Dukes 97 81 75 69 64 47 47 20 6 10 49 60 68 76 25 10 16 12 13 52 Data are from a historically important study conducted by the pioneering public health physician and social statistician Edward Jarvis (1803-1884). Jarvis was an early advocate for the humane treatment of mental illness The source of these data is The Data and Story Library (DASL) story titled "Massachusetts Lunatics" (http://lib.stat.cmu.edu/DASL/Storieslunatics.html). Data are stored online in the file JARVIS.

Explanation / Answer

Regression Analysis: PHOME versus REC_DIST

The regression equation is
PHOME = 80.1 - 310 REC_DIST

Predictor Coef SE Coef T P
Constant 80.063 2.246 35.65 0.000
REC_DIST -310.13 26.11 -11.88 0.000

S = 5.78112 R-Sq = 92.8% R-Sq(adj) = 92.1%

Comment. The p-value of reciprocal of distance is 0.0000 and less than 0.05 level of significance. Hence, the reciprocal of distance is significant at the percent of patients cared for at home and its means that a unit increament of reciprocal of distance decreases 310.13 times in the mean percent of patients cared for at home.

The R-Sq indicate that the 92.8% information of percent of patients cared for at home is explained by reciprocal of distance only.

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