et 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.x8.79.79.88.08.38.7y9.818.620.810.211.413.1Complete parts (a) through (e), given Σx = 53.2, Σy = 83.9, Σx2 = 474.4, Σy2 = 1280.25, Σxy = 759.71, and r ≈ 0.9303.(a) Draw a scatter diagram displaying the data. (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 four 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 answer to four decimal places.)x= y= = + x(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (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 four decimal places. Round your answers for the percentages to two decimal place.)r2 = explained %unexplained %(f) Suppose a small city in Oregon has a per capita income of 8.1 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

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section7.6: The Inverse Trigonometric Functions

Problem 94E

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et 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	8.7	9.7	9.8	8.0	8.3	8.7
y	9.8	18.6	20.8	10.2	11.4	13.1

Complete parts (a) through (e), given Σx = 53.2, Σy = 83.9, Σx² = 474.4, Σy² = 1280.25, Σxy = 759.71, and r ≈ 0.9303.

(a) Draw a scatter diagram displaying the data.

(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 four 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 answer to four decimal places.)

x	=
y	=
	=	+ x

(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.

(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 four decimal places. Round your answers for the percentages to two decimal place.)

r² =
explained	%
unexplained	%

(f) Suppose a small city in Oregon has a per capita income of 8.1 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

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