please answer the whole question (3) 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.x8.29.210.28.08.38.7y9.918.221.010.211.413.1Complete parts (a) through (e), given Σx = 52.6, Σy = 83.8, Σx2 = 464.5, Σy2 = 1275.86, Σxy = 753.01, and r ≈ 0.974.(a) Draw a scatter diagram displaying the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (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 9.3 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

Question
Asked Jul 21, 2019
45 views

please answer the whole question 

(3) 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 9.2 10.2 8.0 8.3 8.7
y 9.9 18.2 21.0 10.2 11.4 13.1
Complete parts (a) through (e), given Σx = 52.6, Σy = 83.8, Σx2 = 464.5, Σy2 = 1275.86, Σxy = 753.01, and r ≈ 0.974.
(a) Draw a scatter diagram displaying the data.

 
Flash Player version 10 or higher is required for this question. 
You can get Flash Player free from Adobe's website.

 

(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 9.3 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

 

check_circle

Expert Answer

Step 1

Hi, since the problem posted by you contains multiple sub-parts, we are answering the first three subparts. If you need any specific sub-part to be answered, please submit that particular sub-pat or specify the subpart number in the message box.

Step 2

Part (a):

The scatter diagram displaying the data is as follows:

help_outline

Image Transcriptionclose

Scatterplot on Y vs X 25 10.2, 21 9.2, 18.2 20 8.7, 13.1 8.3, 114 88.20.09 15 10 6 10 12 X

fullscreen
Step 3

Part (b):

Using calculator, the following preliminary calculations verified.

∑x = (8.2 + 9.2 + 10.2 + 8 + 8.3 + 8.7) = 52.6.

∑x2 = (8.2 2 + 9.22 + 10.22 + 82 + 8.32 + 8.72) = 464.5.

∑y = (9.9 + 18.2 + 21 + 10.2 + 11.4 + 13.1) = 83.8.

∑y2 = (9.92 + 18.2 2 + 212 + 10.22 + 11.42 + 13.12) = 1,275.86.

...
help_outline

Image Transcriptionclose

η(Σw) - (Σs) (Σ) V-Σ )-Σ:)|Σ)-Σν)] 6(753.01)-(52.6)(83.8) M6(464.5) - (52.6) |Ι6(1275.86) - (83.3 ] 4,518.06 4,407.88 (20.24) x (632.72) 110.18 113.1647 =0.9736 κ 0.974

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: A political candidate has asked you to conduct a poll to determine what percentage of people support...

A: As there is no any estimates available, the sample proportion is assumed to be 0.50, that is, 50%.He...

question_answer

Q: How do you calculate a coefficient of correlation of two indexes’ returns?

A: Let the two indexes’ returns be A and B.The coefficient of correlation measures the degree to which ...

question_answer

Q: Why should researchers be very cautious about comparison or correlatios that involve different vaiab...

A: In general correlation does not imply causation. If there is strong correlation between two variable...

question_answer

Q: The Toylot company makes an electric train with a motor that it claims will draw an average of only ...

A: The provided information are:

question_answer

Q: Construct a boxplot for these numbers of state sites for Frogwatch U.S.A Is the distribution symmetr...

A: The given data is arranged in ascending order as shown below199, 235, 238, 242, 253, 289, 294, 314, ...

question_answer

Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have b...

A: Let the random variable X be the white blood cell count per cubic millimetre of whole blood in a hea...

question_answer

Q: Five children aged 2, 3, 5, 7 and 8 years old weigh 14, 20, 32, 42 and 44 kilograms respectively. Fi...

A: Let x be the age of children and y be the weight of children.The equation of the regression line is:

question_answer

Q: Please answer the attached picture. Thanks,

A: Г(1,Ɵ) represents a gamma distribution X~ Г(α,λ) where α is the shape parameter and λ is the scale p...

question_answer

Q: A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters...

A: (a)Poisson distribution is most suitable, when the events are “rare” and occur independently of each...