ASSIGNMENT 01 - JustAnswer



ASSIGNMENT 08

MA270 Statistical Analysis II

Directions: Be sure to make an electronic copy of your answer before submitting. Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be a minimum of one (1) single-spaced page to a maximum of two (2) pages in length; refer to the "Assignment Format" page for specific format requirements.

1. The quarterly production of pine lumber, in millions of board feet, by Northwest Lumber since 1996 is shown in the following table:

| |Quarter |

|Year |Winter |Spring |Summer |Fall |

|1996 |7.8 |10.2 |14.7 |9.3 |

|1997 |6.9 |11.6 |17.5 |9.3 |

|1998 |8.9 |9.7 |15.3 |10.1 |

|1999 |10.7 |12.4 |16.8 |10.7 |

|2000 |9.2 |13.6 |17.1 |10.3 |

a. Determine the typical seasonal pattern for the production data using the ratio-to-moving average method.

The following output is obtained using MEGASTAT:

|  |  |

|  |Data |

|t | Deseasonalized |

|1 |10.33 |

|2 |10.29 |

|3 |10.47 |

|4 |10.95 |

|5 |9.14 |

|6 |11.70 |

|7 |12.46 |

|8 |10.95 |

|9 |11.79 |

|10 |9.79 |

|11 |10.89 |

|12 |11.89 |

|13 |14.17 |

|14 |12.51 |

|15 |11.96 |

|16 |12.60 |

|17 |12.19 |

|18 |13.72 |

|19 |12.18 |

|20 |12.12 |

The linear trend equation is y = 0.142x + 10.11

b. Project the seasonally adjusted production for the four quarters of 2001.

2001 quarter I → y = 0.142x + 10.11→ 0.142(21) + 10.11=13.09

2001 quarter II → y = 0.142x + 10.11→ 0.142(22) + 10.11=13.23

2001 quarter III → y = 0.142x + 10.11→ 0.142(23) + 10.11=13.38

2001 quarter IV → y = 0.142x + 10.11→ 0.142(24) + 10.11=13.52

|Quarter |peroid |Seasonally Unadjusted |Seasonal Index|Seasonally |

| | |Forecast | |Adjusted |

| | | | |Forecast |

|2001 quarter I |21 |13.09 |0.755 |9.88295 |

|2001 quarter II |22 |13.23 |0.991 |13.11093 |

|2001 quarter III |23 |13.38 |1.404 |18.78552 |

|2001 quarter IV |24 |13.52 |0.849 |11.47848 |

2. Sales of roof material, by quarter, since 1994 for Carolina Home Construction, Inc. are shown below (in $000):

| |Quarter |

|Year |I |II |III |IV |

|1994 |210 |180 |60 |246 |

|1995 |214 |216 |82 |230 |

|1996 |246 |228 |91 |280 |

|1997 |258 |250 |113 |298 |

|1998 |279 |267 |116 |304 |

|1999 |302 |290 |114 |310 |

|2000 |321 |291 |120 |320 |

a. Determine the typical seasonal patterns for sales using the ratio-to-moving average method.

The following output is obtained using MEGASTAT:

|  |  |

|  |Data |

|t | Deseasonalized |

|1 |176.3 |

|2 |160.5 |

|3 |137.9 |

|4 |196.5 |

|5 |179.7 |

|6 |192.6 |

|7 |188.5 |

|8 |183.7 |

|9 |206.5 |

|10 |203.2 |

|11 |209.2 |

|12 |223.6 |

|13 |216.6 |

|14 |222.9 |

|15 |259.7 |

|16 |238.0 |

|17 |234.2 |

|18 |238.0 |

|19 |266.6 |

|20 |242.8 |

|21 |253.5 |

|22 |258.5 |

|23 |262.0 |

|24 |247.6 |

|25 |269.5 |

|26 |259.4 |

|27 |275.8 |

|28 |255.6 |

The linear trend equation is y = 4.134x + 163.5

c. Project the sales for 2001, and then seasonally adjust each quarter.

|Quarter |peroid |Seasonally Unadjusted |Seasonal Index|Seasonally |

| | |Forecast | |Adjusted |

| | | | |Forecast |

|2001 quarter I |29 |283.386 |1.919 |543.8177 |

|2001 quarter II |30 |287.52 |1.122 |322.5974 |

|2001 quarter III |31 |291.654 |0.435 |126.8695 |

|2001 quarter IV |32 |295.788 |1.252 |370.3266 |

3. The following is the number of retirees receiving benefits from the State Teachers Retirement System of Ohio from 1991 until 2000:

|Year |Service | |Year |Service | |Year |Service |

|1991 |58,436 | |1995 |67,989 | |1999 |78,341 |

|1992 |59,994 | |1996 |70,448 | |2000 |81,111 |

|1993 |61,515 | |1997 |72,601 | | | |

|1994 |63,182 | |1998 |75,482 | | | |

a. Determine the least squares trend equation. Use a linear equation.

The linear equation is estimated using MEGASTAT:

|Regression Analysis |  |  |  |  |  |

|  | | | | | |  |

|  |r² |0.989 |n |10 | |  |

|  |r |0.995 |k |1 | |  |

|  |Std. Error |883.135 |Dep. Var. |Service | |  |

|  | | | | | |  |

|ANOVA table | | | | | |  |

|Source |SS |df |MS |F |p-value |  |

|Regression | 568,292,827.3485 |1 |568,292,827.3485 |728.65 |3.82E-09 |  |

|Total | 574,532,252.9000 |9 |  |  |  |  |

|  | | | | | |  |

|  | | | | | |  |

|Regression output | | | |confidence interval |

|variables | coefficients |std. error | t (df=8) |p-value |95% lower |95% upper |

Intercept |54,474.7333 |603.2964 | 90.295 |2.53E-13 |53,083.5294 |55,865.9372 | |X1 |2,624.5758 |97.2300 | 26.993 |3.82E-09 |2,400.3629 |2,848.7886 | |

The linear trend equation is y = 2,624.5758 t + 54,474.7333

b. Estimate the number of retirees that will be receiving benefits in 2003. Does this seem like a reasonable estimate based on the historical data?

To estimate the number of retirees that will be receiving benefits in 2003 substitute t = 13 in the above equation:

y = 2,624.5758 t + 54,474.7333 → 2,624.5758 *13 + 54,474.7333 = 88594.218

Yes it is reasonable estimate based on the historical data

c. By how much has the number of retirees increased or decreased (per year) on average during the period?

2,624 retires has been increased on average

This is the end of Assignment 08.

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