Work standards specify time, cost, and efficiency norms for the performance of work tasks. They are typically used to monitor job performance. In the distribution center of McCormick and Co., Inc., data were collected to develop work standards for the time to assemble or fill customer orders. The table below contains data for a random sample of 9 orders. x is the number of cases in the order and y is the time used.
Note: sum x = 1149, sum y = 239, sum x2 = 398979, sum y2 = 11093, sum xy = 58102.
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |
x | 36 | 34 | 255 | 103 | 4 | 555 | 6 | 60 | 96 |
y | 27 | 15 | 71 | 35 | 8 | 60 | 3 | 10 | 10 |
.(a). Find the least squares regression line.
(b). Give a practical interpretation of the slope of the least squares line.
(c). If appropriate, predict the time to fill an order with 600 cases. If not, explain why
(d). Find the residual for Order # 7.
(e). Compute the estimated standard error (s) of the model.
(f). Construct 95% confidence interval estimate of β1.
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