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 8.7 9.0 9.8 8.0 8.3 8.7 y 9.8 18.2 20.6 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.5, Σy = 83.3, Σx2 = 461.31, Σy2 = 1257.25, Σxy = 741.13, and r ≈ 0.878. (a) Draw a scatter diagram displaying the data. Selection Tool (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 (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 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 8.6 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	8.7	9.0	9.8	8.0	8.3	8.7
y	9.8	18.2	20.6	10.2	11.4	13.1

Complete parts (a) through (e), given Σx = 52.5, Σy = 83.3, Σx² = 461.31, Σy² = 1257.25, Σxy = 741.13, and r ≈ 0.878.

(a) Draw a scatter diagram displaying the data.

Selection Tool

(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

(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 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 8.6 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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