| The president of a small manufacturing firm is concerned about the continual increase in manufacturing costs over the past several years. The table below provides a time series of the cost per unit for the firm's leading product over the past eight years. | Year | Quarter | Cost/Unit ($) | | Year | Quarter | Cost/Unit ($) | | 1 | 1 | 20.10 | | 5 | 1 | 28.60 | | | 2 | 17.22 | | | 2 | 32.78 | | | 3 | 13.66 | | | 3 | 28.48 | | | 4 | 17.73 | | | 4 | 25.56 | | 2 | 1 | 20.03 | | 6 | 1 | 25.55 | | | 2 | 25.63 | | | 2 | 35.59 | | | 3 | 22.97 | | | 3 | 26.99 | | | 4 | 29.65 | | | 4 | 28.09 | | 3 | 1 | 23.70 | | 7 | 1 | 28.26 | | | 2 | 20.57 | | | 2 | 28.36 | | | 3 | 26.44 | | | 3 | 32.61 | | | 4 | 25.57 | | | 4 | 28.07 | | 4 | 1 | 20.82 | | 8 | 1 | 37.77 | | | 2 | 28.08 | | | 2 | 28.68 | | | 3 | 32.62 | | | 3 | 37.32 | | | 4 | 25.51 | | | 4 | 37.79 | | (a) | Choose the correct time series plot. | | | | (i) | The line chart shows time series data. The chart has a collection of 32 points connected by linear segments. The coordinates of the points are as follows. - (1,37.79),
- (2,37.32),
- (3,28.68),
- (4,37.77),
- (5,28.07),
- (6,32.61),
- (7,28.36),
- (8,28.26),
- (9,28.09),
- (10,26.99),
- (11,35.59),
- (12,25.55),
- (13,25.56),
- (14,28.48),
- (15,32.78),
- (16,28.6),
- (17,25.51),
- (18,32.62),
- (19,28.08),
- (20,20.82),
- (21,25.57),
- (22,26.44),
- (23,20.57),
- (24,23.7),
- (25,29.65),
- (26,22.97),
- (27,25.63),
- (28,20.03),
- (29,17.73),
- (30,13.66),
- (31,17.22),
- (32,20.1).
| (ii) | The line chart shows time series data. The chart has a collection of 32 points connected by linear segments. The coordinates of the points are as follows. - (1,17.22),
- (2,20.1),
- (3,17.73),
- (4,13.66),
- (5,20.03),
- (6,29.65),
- (7,22.97),
- (8,25.63),
- (9,23.7),
- (10,20.57),
- (11,25.57),
- (12,26.44),
- (13,25.51),
- (14,28.08),
- (15,20.82),
- (16,32.62),
- (17,32.78),
- (18,28.6),
- (19,25.56),
- (20,28.48),
- (21,35.59),
- (22,25.55),
- (23,28.09),
- (24,26.99),
- (25,28.26),
- (26,28.07),
- (27,32.61),
- (28,28.36),
- (29,37.32),
- (30,37.77),
- (31,28.68),
- (32,37.79).
| | | | | | | (iii) | The line chart shows time series data. The chart has a collection of 32 points connected by linear segments. The coordinates of the points are as follows. - (1,28.68),
- (2,37.32),
- (3,37.77),
- (4,37.79),
- (5,28.07),
- (6,28.36),
- (7,28.09),
- (8,28.26),
- (9,32.61),
- (10,25.55),
- (11,35.59),
- (12,26.99),
- (13,25.56),
- (14,28.6),
- (15,32.78),
- (16,28.48),
- (17,20.82),
- (18,25.51),
- (19,28.08),
- (20,32.62),
- (21,25.57),
- (22,20.57),
- (23,26.44),
- (24,29.65),
- (25,23.7),
- (26,25.63),
- (27,22.97),
- (28,17.73),
- (29,17.22),
- (30,13.66),
- (31,20.1),
- (32,20.03).
| (iv) | The line chart shows time series data. The chart has a collection of 32 points connected by linear segments. The coordinates of the points are as follows. - (1,20.1),
- (2,17.22),
- (3,13.66),
- (4,17.73),
- (5,20.03),
- (6,25.63),
- (7,22.97),
- (8,29.65),
- (9,23.7),
- (10,20.57),
- (11,26.44),
- (12,25.57),
- (13,20.82),
- (14,28.08),
- (15,32.62),
- (16,25.51),
- (17,28.6),
- (18,32.78),
- (19,28.48),
- (20,25.56),
- (21,25.55),
- (22,35.59),
- (23,26.99),
- (24,28.09),
- (25,28.26),
- (26,28.36),
- (27,32.61),
- (28,28.07),
- (29,37.77),
- (30,28.68),
- (31,37.32),
- (32,37.79).
| | | | - Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item 1 | | | What type of pattern exists in the data? | | | The time series plot shows a - Select your answer -positivehorizontalverticalnegativeItem 2 - Select your answer -linearnon-linearItem 3 trend with - Select your answer -no apparentpossiblestrongItem 4 seasonality. | | | | | (b) | Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. | | | If required, round your answers for the parameters to four decimal places and your answer for the MSE to three decimal places. Do not round your intermediate calculations. | | | y-intercept, b0 = | | | Slope, b1 = | | | MSE = | | | | | (c) | What is the average cost increase that the firm has been realizing per year? | | | If required, round your answer to two decimal places. | | | $ | | | | | (d) | Compute an estimate of the cost/unit for next year. | | | If required, round your answer to two decimal places. Do not round your intermediate calculations. | | | $ | |
