Question

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 9.0 9.1 9.7 8.0 8.3 8.7 9.7 18.3 21.4 10.2 11.4 13.1 y Complete parts (a) through (e), given Ex = 52.8, Sy = 84.1, Ex2 = 466.48, y2 = 1292.55, Exy 0.796 751.6, and r (a) Draw a scatter diagram displaying the data Tools Actions 22.5 21.5 Clear All 20.5 1. Select an object from the Tools menu to the left. 19.5 Delete O 18.5 17.5 Fill 2. Enter coordinates in Object Properties below, or use the mouse to place and move objects. 16.5 15.5 14.5 To enter a fractional or 13.5 decimal coordinate, use Object Properties No Solution 12.5 11.5 View our tutorial videos 10.5 9.5 8.6 7.5 8.5 9.5 10.5 11.5 Object Properties Select a Tool or Object to Begin Help WebAssign graphing tool (b) Verify the given sums £x, £y, Ex2, £y2, £xy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σχ = Σy Σx2 - Σy2 - Σχy r = a bx. (Round your answers for x and y to (c) Find x, and y. Then find the equation of the least-squares line y = two decimal places. Round your answers for a and b to three decimal places.) х3 y + X point on the line (d) Graph the least-squares line. Be sure to plot the point (x, y) as a 100 Sorry, an error occurred while generating this image. Please return to your home page and open this assignment again. If you still have problems, 50 click Help, and then Contact Us to report this X 2 4. 6 10 error. We are sorry for the inconvenience 50 100 100 50 50 X 2 4. 6 8 10 -50 -50 - (e) Find the value of the coefficient of determination 2. 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.) explained % unexplained (f) Suppose a small city in Oregon has a per capita income of 9.2 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

Answer 1

(y-v (x-x)2 (x-x)(y-Y) Y S.No 0.0400 -0.8633 1 9 9.7 18.6336 2 9.1 18.3 0.0900 18.3469 1.2850 3 0.8100 9.7 21.4 54.5136 6.6450 4 8 10.2 0.6400 14.5669 3.0533 5 8.3 11.4 0.2500 6.8469 1.3083 6 8.7 13.1 0.0100 0.8403 0.0917 Total 1.8400 52.8 84.1 113.7483 11.5200 14.0167 Mean 8.8000 SSX SSY SXY sample size 6 n= here X 14.0167 8.8000 from above '(X-X) 1.8400 '2(X-X)(Y- 11,5200 slope B. Sy/Spm 6.2609 У-В,х- intercept= -41.0790 hence line equation: 6.261 x -41.079 Sy/(VS*Syy) correlation coefficient r= 0.7963

b)

$\sum$x =52.8

$\sum$y =84.1

$\sum$x² =466.48

$\sum$y2=1292.55

$\sum$xy =751.6

r= 0.796

c)

xbar =8.8

ybar =14.02

yhat= -41.079+6.261x

d)

top left curve is correct

e)

r² =0.634

explained =63.4%

unexplained =36.6%

f)predicted number = -41.079+6.261*9.2 =16.52