1 answer

#35 Let x be per capita income in thousands of dollars. Let y be the number...

Question:

#35

Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y.

x 8.2 9.7 9.9 8.0 8.3 8.7
y 10.0 18.7 20.2 10.2 11.4 13.1

Complete parts (a) through (e), given Σx = 52.8, Σy = 83.6, Σx2 = 467.92, Σy2 = 1263.34, Σxy = 753.56, and r ≈ 0.995.

(c) Find x, and y. Then find the equation of the least-squares line y hat = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

x =
y =
y hat = +  x

(e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =
explained     %
unexplained     %

(f) Suppose a small city in Oregon has a per capita income of 9.5 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)
M.D.s per 10,000 residents


Answers

10 18.7 20.2 10.2 11.4 13.1 83.6 13.93 (x-x)? 0.3600 0.8100 1.2100 0.6400 0.2500 0.0100 3.2800 SSX (y-7) 15.4711 22.7211 39.2

c)

xbar =8.80

ybar =13.93

yhat =-34.037+5.451*x

e)

r2 =0.989

explained =98.9%

unexplained =1.1%

f)

predicted value =-34.037+5.451*9.5 =17.75

.

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