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. x 8.2 9.7 10.0 8.0 8.3 8.7 y 9.5 18.7 20.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.9, Σy = 83.1, Σx2 = 469.91, Σy2 = 1253.59, Σxy = 751.48, and r ≈ 0.991. (a) Draw a scatter diagram displaying the data. Get Flash Player 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 y hat = 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 = y hat = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Correct: Your answer is correct. (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 8.8 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

X Values YValues 18.7 20.2 10.2 23 21 19 17 15 13- 10.0 8.0 8.3 13.1 M: 8.8167 M: 13.85 8.6 9.2 10.4 9.8 x-Independent Regression Line (9-5.36X-3343) Estimate Calculation Summary Sum of X-52.9 Sum of Y 83.1 Mean X# 8.8167 Mean Y# 13.85 Sum of squares (SS3.5083 Sum of products (SP) 18.815 Regression Equation-bX+ a b SPISSx 18.82/3.51 5.36295 a = MY-bMX-13.85-(5.36*8.82) =-33.4333 -5.36295X- 33.4333 (X-MxXY- My) Y- M x-Mx2 X-M 0.6167 0.8833 1.1833 0.8167 0.5167 0.1167 -4.35 4.85 6.35 3.65 -2.45 0.75 0.3803 0.7803 1.4003 0.6669 0.2669 0.0136 2.6825 .2842 7.5142 2.9808 1.2658 0.0875 SS: 3.5083 SP: 18.815

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