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# IN THE LEAST-SQUARES LINE = 5 – 6X, WHAT IS THE VALUE OF THE SLOPE?

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Author: Christine Farr
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.In the least-squares line = 5 – 6x, what is the value of the slope? 2. We use the form = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from Climatology Report No. 77-3 of the Department of Atmospheric Science, Colorado State University, showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in Colorado locations.A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 319.59 28.31 11.24 0.002 Elevation -28.167 3.511 -8.79 0.003 S = 11.8603 R-Sq = 95.4% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation = a + bx. (a) Use the printout to write the least-squares equation. = + x (b) For each 1000-foot increase in elevation, how many fewer frost-free days are predicted? (Use 3 decimal places.)(c) The printout gives the value of the coefficient of determination r2. What is the value of r? Be sure to give the correct sign for r based on the sign of b. (Use 3 decimal places.)3. You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some calves to add to the Bar-S herd. How much should a healthy calf weigh? Let x be the age of the calf (in weeks), and let y be the weight of the calf (in kilograms). x3211162636y374977100150200Complete parts (a) through (e), given Σx = 94, Σy = 613, Σx2 = 2362, Σy2 = 82,199, Σxy = 13,756, and r ≈ 0.995.(a) Draw a scatter diagram displaying the data. 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.)

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