Answers
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
#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 = 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 | = | |
![]() | = | + 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
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