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. 8.3 8.7 11.4 13.1 9.6 9.0 9.6 9.8 20.0 8.0 18.9 10.2 A USE SALT Complete parts (a) through (e), given Xx - 53.4, 2y - 83.2, E - 477.78, zy - 1254.98, Exy- 754.03, and r= 0.8482. (a) Draw a scatter diagram displaying the data. Graph Layers After you add an object to the graph you can use Graph Layers to view and edit its properties 12 10 WebAssign. Graching Tool (b) Verify the given sums Ex, Ey, Ex², Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value for r to four decimal places.) Ex Ey = Exy= (c) Find x, and y. Then find the equation of the least-squares line ŷ - a + bx. (Round your answer to four decimal places.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
![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
9.0
Ly 9.6
9.6
18.9 20.0
8.3 8.7
11.4 13.1
9.8
8.0
10.2
A USE SALT
Complete parts (a) through (e), given Ex = 53.4, Ey = 83.2, Ex? - 477.78, Ey² = 1254.98, Exy = 754.03, and r= 0.8482.
(a) Draw a scatter diagram displaying the data.
Graph Layers
After you add an object to the graph you
can use Graph Layers to view and edit its
20
properties.
F
16
15
14
No
Solutien
12
11
10
WebAssign. Graching Tool
(b) Verify the given sums Ex, Ey, Ex?, Ey?, Exy, and the value of the sample correlation coefficient r. (Round your value
for r to four decimal places.)
Ex -
Ey =
Ex? -
Ey -
Exy =
(c) Find x, and y. Then find the equation of the least-squares line ŷ - a+ bx. (Round your answer to four decimal places.)
(d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line.
10아
100
50
50
6
10
2
4
10
O-30
-5아
-5아
y
100
100-
50
5아
2
6
10
6
10
o-50
o-30
(e) Find the value of the coefficient of determination r. 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 to
four decimal places. Round your answers for the percentages to two decimal place.)
2.
explained
unexplained
(f) Suppose a small city in Oregon has a per capita income of 9.9 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3aa1f949-9b51-4eeb-bd19-8a93150eb874%2F473babd8-c260-47a2-8032-be7bf2fa4a25%2Frb6blb6_processed.jpeg&w=3840&q=75)
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