Question

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 8.6 9.7 10.3 8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 = 1344.7, Σxy = 784.51, and r ≈ 0.963.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

Σx =
Σy =
Σx2 =
Σy2 =
Σxy =
r =

(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 r² to 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 8.0 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

Answer 1

Using excel<data<negastat<regression

Here is the output:

Regression Analysis
	r²	0.928
	r	0.963
	Std. Error	1.525
	n	6
	k	1
	Dep. Var.	y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	119.8726	1	119.8726	51.55	.0020
Residual	9.3007	4	2.3252
Total	129.1733	5
Regression output				confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	-35.3360
x	5.549	0.7728	7.180	.0020	3.4032	7.6944

b)

Σx =	53.6
Σy =	85.4
Σx2 =	482.72
Σy2 =	1344.7
Σxy =	784.51
r =	0.963

(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	=8.93
y	=14.23
y cap	=-35.336	+5.549  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 r2 to three decimal places. Round your answers for the percentages to one decimal place.)

r2 =0.928
explained	92.8%
unexplained	7.2%

(f) Suppose a small city in Oregon has a per capita income of 8.0 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

Predicted number=9.05