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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) 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    (b) 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     %  (c) 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

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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) 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
 
 
 
 
(b) 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      %
 
 
(c) 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_circleAnswer
Step 1

(a) Least square regression line:

The least squares regression line can be obtained using EXCEL. Enter the values of x and y in two columns, say in columns A and B in an EXCEL sheet, with the first cell containing the data labels, x and y. Then, follow the procedure given below:

  • Go to Data > Data Analysis > Regression.
  • Enter Input Y Range as $B$2:$B$9 and Input X Range as $A$2:$A$9.
  • Click OK.

The output is as follows:

SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
0.973625036
0.948
Adjusted R Square
Standard Error
0.934932137
1.171462592
Observations
6
ANOVA
Significance F
df
SS
MS
Regression
1
99.96403491 99.96403 72.84285
0.001034284
Residual
5.489298419 1.372325
Total
5
105.4533333
Lower 95%
Lower 95.0%
Coefficients
Standard Error
tStat
p-value
Upper 95%
Upper 95.0%
Intercept
-33.756
5.611978907 -6.01503 0.003847 -49.33757666
18.17487393
-49.33757666
-18.17487393
x Variable 1
0.637820974 8.534802 0,001034
3.672800969
7.214550809
3.672800969
7.214550809
5.444
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SUMMARY OUTPUT Regression Statistics Multiple R R Square 0.973625036 0.948 Adjusted R Square Standard Error 0.934932137 1.171462592 Observations 6 ANOVA Significance F df SS MS Regression 1 99.96403491 99.96403 72.84285 0.001034284 Residual 5.489298419 1.372325 Total 5 105.4533333 Lower 95% Lower 95.0% Coefficients Standard Error tStat p-value Upper 95% Upper 95.0% Intercept -33.756 5.611978907 -6.01503 0.003847 -49.33757666 18.17487393 -49.33757666 -18.17487393 x Variable 1 0.637820974 8.534802 0,001034 3.672800969 7.214550809 3.672800969 7.214550809 5.444

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Step 2

Now, b is the slope of the regression line, which is approximately 5.44 and, a is the “Intercept”, which is approximately -33.756 (rounded to three decimal places).

Therefore, the equation of the least-squares line is = -33.756 +5.44 x.

Step 3

(b) The value of coefficient of determination:

From the EXCEL output in Part (a), the value of coefficient of determination is R-square is 0.948. That is, 94.8% of the va...

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