Question

In: Statistics and Probability

For this activity, select a recurring quantity from your OWN life for which you have monthly...

For this activity, select a recurring quantity from your OWN life for which you have monthly records at least 2 years (including 24 observation in dataset at least). This might be the cost of a utility bill, the number of cell phone minutes used, or even your income. If you do not have access to such records, use the internet to find similar data, such as average monthly housing prices, rent prices in your area for at least 2 years (You must note the data source with an accessible link). Data can also be monthly sales of some particular commodity. 1.4 Please do the descriptive analysis, using the method of index number and Exponential Smoothing individually. And try to explain the pattern you find. 1.5 Use two methods you learned to predict the value of your quantity for the next year (12 months). And make comparison with two results.
MONTHS INTERNET BILL

Jan(2018) 1352

Feb    1434

March    1473

   April 1879
May 3373

June    2249

   July    1327

   August    1536

   September 1810

October 2060

November 3494

December 2399

   Jan(2019) 1410

Feb    1685

March    1724

   April 2223

   May 3794

June 2662

   July 1537

August    1824

September    1888

October    2264

November    3895

December    3124

Solutions

Expert Solution

The Exponential Smoothing method is:

Alpha 0.3
Data Forecasts and Error Analysis
Period Demand Forecast Error Absolute Squared Abs Pct Err
Period 1 1352 1352 0 0 0 00.00%
Period 2 1434 1352 82 82 6724 05.72%
Period 3 1473 1376.6 96.4 96.4 9292.96 06.54%
Period 4 1879 1405.52 473.48 473.48 224183.3 25.20%
Period 5 3373 1547.564 1825.436 1825.436 3332217 54.12%
Period 6 2249 2095.195 153.8052 153.8052 23656.04 06.84%
Period 7 1327 2141.336 -814.336 814.3364 663143.7 61.37%
Period 8 1536 1897.035 -361.035 361.0355 130346.6 23.50%
Period 9 1810 1788.725 21.27518 21.27518 452.6334 01.18%
Period 10 2060 1795.107 264.8926 264.8926 70168.1 12.86%
Period 11 3494 1874.575 1619.425 1619.425 2622537 46.35%
Period 12 2399 2360.403 38.59739 38.59739 1489.758 01.61%
Period 13 1410 2371.982 -961.982 961.9818 925409 68.23%
Period 14 1685 2083.387 -398.387 398.3873 158712.4 23.64%
Period 15 1724 1963.871 -239.871 239.8711 57538.14 13.91%
Period 16 2223 1891.91 331.0902 331.0902 109620.7 14.89%
Period 17 3794 1991.237 1802.763 1802.763 3249955 47.52%
Period 18 2662 2532.066 129.9342 129.9342 16882.9 04.88%
Period 19 1537 2571.046 -1034.05 1034.046 1069251 67.28%
Period 20 1824 2260.832 -436.832 436.8322 190822.4 23.95%
Period 21 1888 2129.783 -241.783 241.7826 58458.81 12.81%
Period 22 2264 2057.248 206.7522 206.7522 42746.47 09.13%
Period 23 3895 2119.273 1775.727 1775.727 3153205 45.59%
Period 24 3124 2651.991 472.0086 472.0086 222792.1 0.1510911
Total 4805.313 13781.86 16339605 592.22%
Average 200.2214 574.2441 680816.9 24.68%
Bias MAD MSE MAPE
SE 861.8058
Next period 2793.59399

The regression method is:

r² 0.163
r   0.404
Std. Error   747.260
n   24
k   1
Dep. Var. Data
ANOVA table
Source SS   df   MS F p-value
Regression 23,93,544.5435 1   23,93,544.5435 4.29 .0504
Residual 1,22,84,729.4565 22   5,58,396.7935
Total 1,46,78,274.0000 23  
Regression output confidence interval
variables coefficients std. error    t (df=22) p-value 95% lower 95% upper
Intercept 1,613.7283
t 45.6217 22.0355 2.070 .0504 -0.0771 91.3205
Predicted values for: Data
t Predicted
25 2,754.272
26 2,799.893
27 2,845.515
28 2,891.137
29 2,936.759
30 2,982.380
31 3,028.002
32 3,073.624
33 3,119.246
34 3,164.867
35 3,210.489
36 3,256.111

The regression method is better because it has lower MSE value.

orchestra answered 1 year ago
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