Question

Ohio Swiss Milk Products manufactures and distributes ice cream in Ohio, Kentucky, and West Virginia. The company wants to expand operations by locating another plant in northem Ohio. The size of the new plant will be a function of the expected demand for los crean within the area served by the plant. A market survey is currently under way to determine that demand. Ohio Swiss wants to estimate the relationship between the manufacturing cost per gallon and the number of gallons sold in a year to determine the demand for ice cream and, thus, the size of the new plant. The following data have been collected: Plant Cost per Thousand Gallons M $03 951 1033 1.005 1080 1068 DAS 997 1056 1000 $10,160 Thousands of Galion Sold 4036 4813 2479 3721 2150 250 6186 4140 240 395.6 36506 Total Develop a regression in to forecast the cost per thousand alone auction of the number of thousands of gallons produced The forecasting model is given by the equation Y - X. (Enter your responses rounded to the decimal places) b. What are the correlation coefficient and the coefficient of determination

Answer 1

Answer(b): The correlation coefficient between two variables is given by following formula E(y-y)*(x-x) r = LAUAN =(y-7)?? (x– x)? r = Cost per Thousands y-ý x- y - y) (x (y-7) thousand of gallons * (x-) Plant gallons (v) sold (x) 993 403.6 -23.90 38.54 -921.11 1485.33 571.21 951 481.3 -65.90 116.24 -7660.22 13511.74 4342.81 1033 247.9 16.10 -117.16 -1886.28 13726.47 259.21 1006 372.1 -10.90 7.04 -76.74 49.56 118.81 1080 215.9 63.10 -149.16 -9412.00 22248.71 3981.61 1068 258.6 51.10 -106.46 -5440.11 11333.73 2611.21 985 618.6 -31.90 253.54 -8087.93 64282.53 1017.61 997 414 -19.90 48.94 -973.91 2395.12 396.01 1056 243 39.10 -122.06 -4772.55 14898.64 1528.81 10 1000 395.6 -16.90 30.54 -516.13 932.69 285.61 Total 10169 3650.6 0.00 -39746.94 144864.52 15112.90 Mean 1016.9 365.06 Answer(a): The regression equation between two variables to forecast the cost per thousand as a function of thousands of gallons sold can be given by following equation y=b0+ b1 * x The estimate of b0 and b1 can be obtained by least square method. The least square estimate of bl can be given by following expression E(y-7)+ (x - 2) b1 = - {(x-) ? -39746.94 V 144864.52 * 15112.90 -39746.94 r= 46790.2 r=-0.85 The coefficient of correlation between Cost per thousand gallons and Thousands of gal- lons sold is -0.85 The coefficient of determination is given by r2 = -0.85*-0.85 r2 = 0.72 The coefficient of determination is 0.72 b1 =-39746.94 The increase in X mostly result in Decrease in Y. Also 72% of the variation is explained by X 144864.52 b1 = -0.27437 The estimate of b0 can be given by bo=y-b1*X b0 = 1016.9-(-0.27437) * 365.06 b0 = 1117.063 The final estimated equation of line can be given as y=1117.06 + 0.27*X Cost per thousand gallons = 1117.06 – 0.27 * Thousands of gallons sold Answer(c): Here we have demand of 325000 gallons i.e x= 325 If we have x=325, then estimate of y can be obtained by estimated equation Cost per thousand gallons = 1117.06 -0.27 * 325 Cost per thousand gallons = 1117.06 - 89.1713 Cost per thousand gallons = 1027.89 The forecasted manufacturing cost per gallon is $1027.89. C .