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 3 10 16 26 36 y 46 51 74100 150 200 Complete parts (a) through (e), given ?x = 92, ?y =621, ?x2 = 2338, ?y2 = 82,693, ?xy = 13,639, and r ? 0.996. (a)Draw a scatter diagram displaying the data. (b) Verify the givensums ?x, ?y, ?x2, ?y2, ?xy, and the value of the sample correlationcoefficient r. (Round your value for r to three decimal places.) ?x= ?y = ?x2 = ?y2 = ?xy = r = (c) Find x, and y. Then find theequation of the least-squares line y hat = a + bx. (Round youranswers for x and y to two decimal places. Round your answers for aand b to three decimal places.) x = y = y hat = + x (d) Graph theleast-squares line. Be sure to plot the point (x, y) as a point onthe line. WebAssign Plot WebAssign Plot WebAssign Plot WebAssignPlot (e) Find the value of the coefficient of determination r2.What percentage of the variation in y can be explained by thecorresponding variation in x and the least-squares line? Whatpercentage is unexplained? (Round your answer for r2 to threedecimal places. Round your answers for the percentages to onedecimal place.) r2 = explained % unexplained % (f) The calves youwant to buy are 12 weeks old. What does the least-squares linepredict for a healthy weight? (Round your answer to two decimalplaces.) kg
