Question

15. -1.16 points BBUnderStat12 9.2.013. /100 Submissions Used My Notes Ask Your 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 Complete parts (a) through (e), given Σχ " 532, Σ,. 842 Σκ2 474 B, Zy2-1297 98Lxy 76404, and r #0921. (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 ΣΧ Ex Er2·Er2Ly, and the value of the sample correlation coefficient r (Round your value for r to three decimal places.) Er Exy (c) Find x, and y Then find the equation of the least-squares lne a+bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) (d) Graph the least-squares line. Be sure to plot the point .y) as a point on the line 100 100 50 50 10 100 100 50 50 lo (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) () Suppose a small city in Oregon has a per capita income of 8.0 thousand dolars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.) M.Ds per 10,000 residents

Answer 1

(a)

25 20 15 พู 10 10 12

(b)

9.6 18.5 21.4 10.2 11.4 13.1 x 2 75.69 86.49 104.04 64 68.89 75.69 xy (xxbar)2 (y-ybar)2 xb)(y-y-bar) ' (Predicted y)bar)42 (y-y)2 12.1957 4.0797 0.0263 1.1243 0.3208 0.0001 13.0922 16.4802 21.5621 9.1397 10.8336 13.0922 8.7 9.3 10.2 92.16 342.25 457.96 104.04 129.96 171.61 0.7389 1.9356 9.8222 3.3222 1.4922 0.1556 0.8857 5.9870 56.6819 23.9481 10.2382 0.8857 81.6 8.3 8.7 n- Sums Means 53.2 84.2 474.8 1297.98 764.04 3.09333333 116.373333 17.46666667 98.6264 17.7469 14.03333333

All values are verified

(c)

x-bar = 8.87, y-bar = 14.03

SS(x) = Σ[(x - x-bar)^2] OR Σ(x^2) - [(Σx)^2 /n] = 3.0933   

SS(y) = Σ[(y - y-bar)^2] OR Σ(y^2) - [(Σy)^2 /n] = 116.3733   

SS(xy) = Σ[(x - x-bar)(y - y-bar)] OR Σ(xy) - [(Σx)(Σy)/n] = 17.4667   

Correlation coefficient, r = SSxy / √[SS(x) * SS(y)] = 0.9206   

Coefficient of determination = r^2 = 0.8475

Slope of the regression line is b = SS(xy)/SS(x) = 5.6466   

Intercept of the regression line is a = y-bar - b * x-bar = -36.0328   

The regression equation is y = a + bx, that is y-hat = -36.033 + 5.647 x

(d)

36.033+5.647%:0 15 10 -5 deadline

(e) r^2 = 0.848

Explained = 84.8%, Unexplained = 15.2%

(f) When x = 8, y-hat = -36.033 + 5.647(8) = 9.14

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