Question

In: Statistics and Probability

Let x be per capita income in thousands of dollars. Let y be the number of...

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 8.6 9.7 10.3 8.0 8.3 8.7 y 9.7 19.0 22.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.6, Σy = 85.4, Σx2 = 482.72, Σy2 = 1344.7, Σxy = 784.51, and r ≈ 0.963.

(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

(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 8.0 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

Solutions

Expert Solution

Using excel<data<negastat<regression

Here is the output:

Regression Analysis
0.928
r   0.963
Std. Error   1.525
n   6
k   1
Dep. Var. y
ANOVA table
Source SS   df   MS F p-value
Regression 119.8726 1   119.8726 51.55 .0020
Residual 9.3007 4   2.3252
Total 129.1733 5  
Regression output confidence interval
variables coefficients std. error    t (df=4) p-value 95% lower 95% upper
Intercept -35.3360
x 5.549 0.7728 7.180 .0020 3.4032 7.6944

b)

Σx = 53.6
Σy = 85.4
Σx2 = 482.72
Σy2 = 1344.7
Σxy = 784.51
r = 0.963

(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 =8.93
y =14.23
y cap =-35.336 +5.549  x

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 =0.928
explained     92.8%
unexplained     7.2%


(f) Suppose a small city in Oregon has a per capita income of 8.0 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

Predicted number=9.05


Related Solutions

Let x be per capita income in thousands of dollars. Let y be the number of...
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 9.4 10.2 8.0 8.3 8.7 y 9.5 18.0 21.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.6, Σy = 83.4, Σx2 = 481.98, Σy2 = 1269.3, Σxy = 761.13, and r ≈ 0.864. (b) Verify the given sums Σx, Σy,...
Let x be per capita income in thousands of dollars. Let y be the number of...
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 8.4 9.1 9.8 8.0 8.3 8.7 y 9.8 18.4 21.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.3, Σy = 84.1, Σx2 = 457.99, Σy2 = 1289.65, Σxy = 747.71, and r ≈ 0.958. (a) Draw a scatter diagram displaying the...
Let x be per capita income in thousands of dollars. Let y be the number of...
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 8.3 9.3 10.2 8.0 8.3 8.7 y 9.9 18.1 20.6 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.8, Σy = 83.3, Σx2 = 468, Σy2 = 1255.59, Σxy = 750.81, and r ≈ 0.974. (a) Draw a scatter diagram displaying the...
We have 2008 data on y = income per capita (in thousands of dollars) and x...
We have 2008 data on y = income per capita (in thousands of dollars) and x = percentage of the population with a bachelor’s degree or more for the 50 U.S. states plus the District of Columbia, a total of N = 51 observations. We have results from a simple linear regression of y on x. a. The estimated error variance is ?̂ 2 = 14.24. What is the sum of squared least squares residuals? b. The estimated variance of...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $22.6$ for a random sample of 2692 people. Assume the population standard deviation is known to be $12.4$. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $⁢22.4 for a random sample of 2128 people. Assume the population standard deviation is known to be $⁢9.3. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $23.6$⁢23.6 for a random sample of 12341234 people. Assume the population standard deviation is known to be $11.4$⁢11.4. Construct the 90%90% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $36.6 for a random sample of 1012 people. Assume the population standard deviation is known to be $8.5. Construct the 80% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
An economist wants to estimate the mean per capita income (in thousands of dollars) for a...
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $23.1 for a random sample of 3231 people. Assume the population standard deviation is known to be $11.8. Construct the 95% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
An economist wants to estimate the mean per capita income (in thousands of dollars). Suppose that...
An economist wants to estimate the mean per capita income (in thousands of dollars). Suppose that the mean income is found to be $23.4 $23.4 for a random sample of 976 976 people. Assume the population standard deviation is known to be $10 $10. Construct the 95% 95% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT