You are the foreman of the Bar-S cattle ranch in Colorado. Aneighboring ranch has calves for sale, and you are going to buysome calves to add to the Bar-S herd. How much should a healthycalf weigh? Let x be the age of the calf (in weeks), and let y bethe weight of the calf (in kilograms). x 1 5 11 16 26 36 y 39 47 73100 150 200 Complete parts (a) through (e), given Σx = 95, Σy =609, Σx2 = 2375, Σy2 = 81,559, Σx y = 13,777, and r ≈ 0.997. (a)Make a scatter diagram of the data.

(Select the correct graph.) A scatter diagram with 6 points isgraphed on the x y coordinate plane. The points are located at (1,39), (5, 47), (11, 73), (16, 100), (26, 150), (36, 200). Whenconsidering the data points as a whole, the points are looselygathered into a mass that is lower on the left and higher on theright. A scatter diagram with 6 points is graphed on the x ycoordinate plane. The points are located at (1, 29), (5, 37), (11,63), (16, 90), (26, 140), (36, 190). When considering the datapoints as a whole, the points are loosely gathered into a mass thatis lower on the left and higher on the right. A scatter diagramwith 6 points is graphed on the x y coordinate plane. The pointsare located at (3, 39), (7, 47), (13, 73), (18, 100), (28, 150),(38, 200). When considering the data points as a whole, the pointsare loosely gathered into a mass that is lower on the left andhigher on the right. A scatter diagram with 6 points is graphed onthe x y coordinate plane. The points are located at (3, 29), (7,37), (13, 63), (18, 90), (28, 140), (38, 190). When considering thedata points as a whole, the points are loosely gathered into a massthat is lower on the left and higher on the right. (b) Verify thegiven sums Σx, Σy, Σx2, Σy2, Σx y, and the value of the samplecorrelation coefficient r. (For each answer, enter a number. Roundyour value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x bar, and y bar. Then find the equation of theleast-squares line y hat = a + b x. (For each answer, enter anumber. Round your answers for x bar and y bar to two decimalplaces. Round your answers for a and b to three decimal places.) xbar = x bar = y bar = y bar = y hat = value of a coefficient +value of b coefficient x (d) Graph the least-squares line. Be sureto plot the point (x bar, y bar) as a point on the line. (Selectthe correct graph.) A line and a point are graphed on the x ycoordinate plane. The point is located the approximate point (15.8,102). The line enters the window at approximately y = 171 on thepositive y axis, goes down and right, passes through theapproximate point (15.8, 102), and exits the window atapproximately x = 39.1 on the positive x axis. A line and a pointare graphed on the x y coordinate plane. The point is located theapproximate point (15.8, 132). The line enters the window atapproximately y = 201 on the positive y axis, goes down and right,passes through the approximate point (15.8, 132), and exits thewindow in the first quadrant. A line and a point are graphed on thex y coordinate plane. The point is located the approximate point(15.8, 132). The line enters the window at approximately y = 56 onthe positive y axis, goes up and right, passes through theapproximate point (15.8, 132), and exits the window in the firstquadrant. A line and a point are graphed on the x y coordinateplane. The point is located the approximate point (15.8, 102). Theline enters the window at approximately y = 26 on the positive yaxis, goes up and right, passes through the approximate point(15.8, 102), and exits the window in the first quadrant. (e) Findthe value of the coefficient of determination r2. What percentageof the variation in y can be explained by the correspondingvariation in x and the least-squares line? What percentage isunexplained? (For each answer, enter a number. Round your answerfor r2 to three decimal places. Round your answers for thepercentages to one decimal place.) r2 = explained = % unexplained =% (f) The calves you want to buy are 21 weeks old. What does theleast-squares line predict for a healthy weight (in kg)? (Enter anumber. Round your answer to two decimal places.) kg