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Exhibit I Production of Electric fans in India (in lakh numbers) Month Apr May June July Aug Sept Oct Nov Dec Jan Feb Mar 2000-01 2001-02 2002-03...

Question 1
1.
From the line chart of the actual data, which of the following statements is false?
Answer

A clear multiplicative trend is visible

A clear monthly seasonal pattern is visible

Noise or random pattern is clearly visible

Data heteroscedasticity is clearly visible

Observing a cyclical component is irrelevant
1 points
Question 2
1.
Calculate the correlation coefficient between the ln(Production) and time variable; which of the following statements is true:
Answer

The correlation coefficient is not statistically significant at 5% level

The correlation coefficient is not statistically significant at 10% level

The correlation coefficient is statistically significant with 95% confidence

Ln(Production) is independent from time variable

The correlation coefficient is 69%
1 points
Question 3
1.
The meaning of the regression coefficient for the dummy variable for January is
Answer

This value has no meaning

An error of 12.6% is detected by the regression

The actual number of fans produced were 12.6% higher than expected

The actual number of fans produced were 113,460 higher than predicted annual average

This month was over-forecast by the regression model
1 points
Question 4
1.
Using the regression model, the forecast value for January 2009 in lakh number is about
Answer

2.37

10.1

10.5

10.7

12.6
1 points
Question 5
1.
Which of the following statements is false:
Answer

The regression coefficients are statistically significant at 1% level

The regression coefficients are statistically significant at 5% level

The regression coefficients are statistically significant at 10% level

The explained variation is about 67%

The unexplained variation is about 31%
1 points
Question 6
1.
Which of the following statements describes the regression forecast the best:
Answer

The regression forecast is best suited for series exhibiting linear trend

The regression forecast is best suited for series exhibiting seasonal variation

The regression forecast is best suited for series exhibiting additive cyclical pattern

The regression forecast is best suited for series with additive trend and additive seasonality

The regression forecast is best suited for the series with additive trend and multiplicative seasonality
1 points
Question 7
1.
Which of the following statements about the error metrics of the estimated Production forecast is false:
Answer

The root mean squared error is 0.74 in lakh number

The mean absolute percent error is about 7.2%

The size of the systematic overforecast is 0.035

The size of systematic underforecast is 3549 electric fans per month

The Thiel s U statistics is about 0.94
1 points
Question 8
1.
Which of the following statements is true
Answer

Naïve forecast is better than the forecast produced by the regression model

Naïve forecast is equivalent to the forecast produced by the regression model

The regression model does not have any substantial bias

The regression model produces good forecast because the average error is less than 5%

The regression model produces good forecast because the average residual is less than 5%
1 points
Question 9
1.
The residuals of the regression model are approximately normally distributed because
Answer

The residual excess kurtosis is about 3

The skewness of the residuals is less than 0.0

The mean, the median, and the mode of the residuals are distinctly different

The residual plot displays the typical bell-shaped distribution

The skewness, excess kurtosis, and measures of central tendency of the regression residuals are all approximately 0.0
1 points
Question 10
1.
The following statement is not true about the regression residuals:
Answer

The residuals are approximately normally distributed

The residuals are approximately triangularly distributed

There is no pattern between residuals and the predicted value of the series

The mean residual is zero

The variance of the standardized residuals is one
1 points

Exhibit I Production of Electric fans in India (in lakh numbers) Month 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 2006-07 2007-08 2008-09 Apr 6.6 6.9 7.7 9 9.2 9.6 9.7 10.1 10.4 May 6.7 7.3 8.1 8.5 9.5 9.7 10.1 11.3 11.6 June 5.9 7.2 8.7 8.7 7.9 8.8 9.9 10.8 10.7 July 4.9 7.2 8.2 7.2 7 9.7 9.1 9.7 9.5 Aug 5.8 7.2 6.8 8.1 6.1 6.9 8.9 8.8 8.8 Sept 6.4 7.5 6.5 7.7 6.6 7.5 8.6 8.4 8.9 Oct 6.2 7.2 7.6 8.5 6.8 7.3 8.2 8.1 8.4 Nov 6.3 7.4 7.7 8.2 7 7.7 8.8 8.6 7.6 Dec 9.6 7.1 7.7 8.3 8.2 8.8 9.4 9.7 8.2 Jan 7.5 7.8 7.6 8.2 8.9 9.4 10.5 10.3 Feb 7.6 8.1 7.3 8.3 9.8 10.2 10.9 10.6 Mar 8.1 8.7 8 9.3 10.2 11.8 11.1 10.9
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Month Year Production Independent X Variables Forecast Error Metrics Calcs lnProduction time Jan Feb Mar Apr May Jun e e^2 APE Num Den Apr 2000 6.6 1.887069649 1 0 0 0 1 0 0 1405.283378 -1398.6833776 1956315.1908 211.9217 100252.5 0.00023 May 2000 6.7 1.9021075264 2 0 0 0 0 1 0 2096.43645 -2089.7364499 4366998.4301 311.901 38156.22 0.014257 ME -8721.168958 June 2000 5.9 1.7749523509 3 0 0 0 0 0 1 1314.652416 -1308.7524157 1712832.8856 221.8224 6742.197 0.028727 MSE 198448483.9 July 2000 4.9 1.5892352051 4 0 0 0 0 0 0 489.3541923 -484.45419234 234695.86447 98.8682 10397.14 0.033736 RMSE 14087.174447 Aug 2000 5.8 1.7578579176 5 0 0 0 0 0 0 505.4352807 -499.63528072 249635.41374 86.14401 7903.971 0.010702 MAPE 910.07410867 Sept 2000 6.4 1.8562979904 6 0 0 0 0 0 0 522.0448236 -515.64482356 265889.58406 80.5695 6935.771 0.000977 Thiel's U 13313.33078 Oct 2000 6.2 1.8245492921 7 0 0 0 0 0 0 539.2001869 -533.00018685 284089.19918 85.96777 7887.139 0.00026 Nov 2000 6.3 1.8405496334 8 0 0 0 0 0 0 556.9193073 -550.61930727 303181.62154 87.39989 8060.64 0.274376 Coef icient Dec 2000 9.6 2.2617630985 9 0 0 0 0 0 0 575.2207109 -565.62071092 319926.78862 58.91882 29775.14 0.047852 Regression Table Jan 2001 7.5 2.0149030205 10 1 0 0 0 0 0 1664.025544 -1656.5255436 2744076.8765 220.8701 93673.73 0.000178 Constant 6.0637527348 Feb 2001 7.6 2.0281482473 11 0 1 0 0 0 0 2303.062348 -2295.462348 5269147.3911 302.0345 344229.4 0.004328 time 0.032333453 Mar 2001 8.1 2.0918640617 12 0 0 1 0 0 0 4467.101181 -4459.0011815 19882691.536 550.494 64964.1 0.021948 Jan 1.0299077067 Apr 2001 6.9 1.9315214116 13 0 0 0 1 0 0 2071.43253 -2064.5325297 4262294.5664 299.2076 199629.5 0.003361 Feb 1.3225742536 May 2001 7.3 1.9878743482 14 0 0 0 0 1 0 3090.214207 -3082.9142074 9504360.01 422.317 69945 0.000188 Mar 1.9527408006 June 2001 7.2 1.974081026 15 0 0 0 0 0 1 1937.839601 -1930.6396006 3727369.2674 268.1444 9837.435 0 Apr 1.1519080658 July 2001 7.2 1.974081026 16 0 0 0 0 0 0 721.3236908 -714.12369081 509972.64577 99.18385 10501.35 0 May 1.5195746128 Aug 2001 7.2 1.974081026 17 0 0 0 0 0 0 745.0277281 -737.8277281 544389.75635 102.4761 11201.01 0.001736 Jun 1.0205744931 Sept 2001 7.5 2.0149030205 18 0 0 0 0 0 0 769.5107241 -762.01072412 580660.34368 101.6014 11027.75 0.0016 Oct 2001 7.2 1.974081026 19 0 0 0 0 0 0 794.7982769 -787.5982769 620311.04578 109.3886 12766.39 0.000772 Nov 2001 7.4 2.0014800002 20 0 0 0 0 0 0 820.9168257 -813.51682567 661809.62565 109.9347 12909.68 0.001644 Dec 2001 7.1 1.960094784 21 0 0 0 0 0 0 847.8936785 -840.7936785 706934.00981 118.4216 118590.7 0.00972 Jan 2002 7.8 2.0541237337 22 1 0 0 0 0 0 2452.826737 -2445.0267367 5978155.7433 313.465 188521.6 0.001479 Feb 2002 8.1 2.0918640617 23 0 1 0 0 0 0 3394.787373 -3386.6873729 11469651.362 418.1096 659093.3 0.005487 Mar 2002 8.7 2.1633230257 24 0 0 1 0 0 0 6584.64965 -6575.9496503 43243113.803 755.8563 122552.9 0.013212 Apr 2002 7.7 2.0412203289 25 0 0 0 1 0 0 3053.357631 -3045.6576314 9276030.4075 395.54 348709.3 0.002699 May 2002 8.1 2.0918640617 26 0 0 0 0 1 0 4555.074325 -4546.9743252 20674975.514 561.3549 123603.2 0.005487 June 2002 8.7 2.1633230257 27 0 0 0 0 0 1 2856.437392 -2847.7373919 8109608.2535 327.3261 14706.56 0.003303 July 2002 8.2 2.1041341543 28 0 0 0 0 0 0 1063.254132 -1055.0541318 1113139.2211 128.6651 17714.79 0.029149 Aug 2002 6.8 1.9169226122 29 0 0 0 0 0 0 1098.194639 -1091.394639 1191142.258 160.4992 27506.39 0.001946 Sept 2002 6.5 1.8718021769 30 0 0 0 0 0 0 1134.283356 -1127.7833562 1271895.2985 173.5051 32066.23 0.028639 Oct 2002 7.6 2.0281482473 31 0 0 0 0 0 0 1171.558016 -1163.9580157 1354798.2623 153.1524 25028.8 0.000173 Nov 2002 7.7 2.0412203289 32 0 0 0 0 0 0 1210.05759 -1202.3575898 1445663.7738 156.1503 26022.4 0 Dec 2002 7.7 2.0412203289 33 0 0 0 0 0 0 1249.822331 -1242.1223315 1542867.8864 161.3146 219552.5 0.000169 Jan 2003 7.6 2.0281482473 34 1 0 0 0 0 0 3615.54486 -3607.9448597 13017266.11 474.7296 432258.6 0.001558 Feb 2003 7.3 1.9878743482 35 0 1 0 0 0 0 5004.024888 -4996.7248877 24967259.603 684.4829 1764888 0.009195 Mar 2003 8 2.0794415417 36 0 0 1 0 0 0 9705.983647 -9697.983647 94050886.818 1212.248 315246.7 0.015625 Apr 2003 9 2.1972245773 37 0 0 0 1 0 0 4500.746556 -4491.7465564 20175787.127 499.083 555161.6 0.003086 May 2003 8.5 2.1400661635 38 0 0 0 0 1 0 6714.324871 -6705.8248707 44968087.196 788.9206 244359.2 0.000554 June 2003 8.7 2.1633230257 39 0 0 0 0 0 1 4210.479841 -4201.7798414 17654953.835 482.9632 32155.11 0.029727 July 2003 7.2 1.974081026 40 0 0 0 0 0 0 1567.27051 -1560.0705101 2433819.9964 216.6765 50043.8 0.015625 Aug 2003 8.1 2.0918640617 41 0 0 0 0 0 0 1618.773932 -1610.6739323 2594270.5162 198.8486 42216.04 0.002439 Sept 2003 7.7 2.0412203289 42 0 0 0 0 0 0 1671.969853 -1664.2698527 2769794.1427 216.1389 49805.13 0.010794 Oct 2003 8.5 2.1400661635 43 0 0 0 0 0 0 1726.91389 -1718.41389 2952946.2973 202.1663 43630.04 0.001246 Nov 2003 8.2 2.1041341543 44 0 0 0 0 0 0 1783.66349 -1775.4634905 3152270.6059 216.5199 50021.94 0.000149 Dec 2003 8.3 2.1162555148 45 0 0 0 0 0 0 1842.277988 -1833.9779883 3363475.2614 220.9612 411024.4 0.000145 Jan 2004 8.2 2.1041341543 46 1 0 0 0 0 0 5329.428466 -5321.2284657 28315472.384 648.9303 807322.5 0.000149 Feb 2004 8.3 2.1162555148 47 0 1 0 0 0 0 7376.092322 -7367.7923221 54284363.701 887.6858 2967371 0.014516 Mar 2004 9.3 2.2300144002 48 0 0 1 0 0 0 14306.92953 -14297.629535 204422210.31 1537.38 507471.5 0.000116 Apr 2004 9.2 2.2192034841 49 0 0 0 1 0 0 6634.244006 -6625.0440063 43891208.085 720.1135 1155071 0.001063 May 2004 9.5 2.2512917986 50 0 0 0 0 1 0 9897.129059 -9887.6290587 97765208.403 1040.803 425719.4 0.028366 June 2004 7.9 2.0668627595 51 0 0 0 0 0 1 6206.381608 -6198.4816083 38421174.248 784.6179 84998.58 0.012979 July 2004 7 1.9459101491 52 0 0 0 0 0 0 2310.206731 -2303.2067307 5304761.2442 329.0295 115602.4 0.016531 Aug 2004 6.1 1.8082887712 53 0 0 0 0 0 0 2386.124418 -2380.0244181 5664516.2308 390.1679 162361 0.006719 Sept 2004 6.6 1.887069649 54 0 0 0 0 0 0 2464.536902 -2457.9369019 6041453.8136 372.4147 147959.8 0.000918 Oct 2004 6.8 1.9169226122 55 0 0 0 0 0 0 2545.526166 -2538.7261656 6445130.5439 373.3421 148698.3 0.000865 Nov 2004 7 1.9459101491 56 0 0 0 0 0 0 2629.176887 -2622.1768871 6875811.6272 374.5967 149589.5 0.029388 Dec 2004 8.2 2.1041341543 57 0 0 0 0 0 0 2715.576527 -2707.3765268 7329887.6578 330.1679 915720.1 0.007287 Jan 2005 8.9 2.1860512767 58 1 0 0 0 0 0 7855.747577 -7846.8475771 61573016.898 881.6683 1489715 0.010226 Feb 2005 9.8 2.2823823857 59 0 1 0 0 0 0 10872.59539 -10862.795394 118000323.77 1108.449 4626305 0.001666 Mar 2005 10.2 2.3223877203 60 0 0 1 0 0 0 21088.87055 -21078.670551 444310352.22 2066.536 917367.2 0.00346 Apr 2005 9.6 2.2617630985 61 0 0 0 1 0 0 9779.08731 -9769.4873099 95442882.299 1017.655 2306280 0.000109 May 2005 9.7 2.2721258855 62 0 0 0 0 1 0 14588.68397 -14578.983969 212546773.58 1502.988 887792.2 0.008609 June 2005 8.8 2.1747517215 63 0 0 0 0 0 1 9148.404486 -9139.6044857 83532370.154 1038.591 148892.4 0.01046 July 2005 9.7 2.2721258855 64 0 0 0 0 0 0 3405.318421 -3395.6184209 11530224.46 350.0638 130963.7 0.083324 Aug 2005 6.9 1.9315214116 65 0 0 0 0 0 0 3517.223514 -3510.3235141 12322371.173 508.7425 276052.2 0.007561 Sept 2005 7.5 2.0149030205 66 0 0 0 0 0 0 3632.806017 -3625.3060166 13142843.714 483.3741 249318.7 0.000711 Oct 2005 7.3 1.9878743482 67 0 0 0 0 0 0 3752.186775 -3744.8867751 14024176.958 512.9982 280724.4 0.003002 Nov 2005 7.7 2.0412203289 68 0 0 0 0 0 0 3875.490607 -3867.7906072 14959804.181 502.3105 269057.3 0.020408 Dec 2005 8.8 2.1747517215 69 0 0 0 0 0 0 4002.846432 -3994.0464324 15952406.904 453.8689 1728694 0.004649 Jan 2006 9.4 2.2407096893 70 1 0 0 0 0 0 11579.62254 -11570.222541 133870049.66 1230.875 2903164 0.007243 Feb 2006 10.2 2.3223877203 71 0 1 0 0 0 0 16026.55247 -16016.352466 256523546.33 1570.231 9280904 0.024606 Mar 2006 11.8 2.4680995315 72 0 0 1 0 0 0 31085.66797 -31073.867967 965585270.42 2633.379 1490259 0.031672 Apr 2006 9.7 2.2721258855 73 0 0 0 1 0 0 14414.68667 -14404.986666 207503640.84 1485.05 4910147 0.0017 May 2006 10.1 2.3125354238 74 0 0 0 0 1 0 21504.18558 -21494.085577 461995714.78 2128.127 1780016 0.000392 June 2006 9.9 2.2925347571 75 0 0 0 0 0 1 13485.04006 -13475.140063 181579399.71 1361.125 256143.1 0.00653 July 2006 9.1 2.2082744135 76 0 0 0 0 0 0 5019.547988 -5010.4479883 25104589.044 550.5987 323473.4 0.000483 Aug 2006 8.9 2.1860512767 77 0 0 0 0 0 0 5184.499666 -5175.5996657 26786831.899 581.5281 360846.2 0.001136 Sept 2006 8.6 2.1517622033 78 0 0 0 0 0 0 5354.871962 -5346.2719618 28582623.889 621.6595 412379.5 0.002163 Oct 2006 8.2 2.1041341543 79 0 0 0 0 0 0 5530.843008 -5522.6430082 30499585.796 673.493 483838.5 0.005354 Nov 2006 8.8 2.1747517215 80 0 0 0 0 0 0 5712.59679 -5703.7967903 32533297.825 648.1587 448127.3 0.004649 Dec 2006 9.4 2.2407096893 81 0 0 0 0 0 0 5900.32334 -5890.9233396 34702977.792 626.694 3293157 0.013694 Jan 2007 10.5 2.3513752572 82 1 0 0 0 0 0 17068.73304 -17058.233038 290983314.36 1624.594 5057251 0.001451 Feb 2007 10.9 2.3887627892 83 0 1 0 0 0 0 23623.64961 -23612.749612 557561944.24 2166.307 17663255 0.000337 Mar 2007 11.1 2.4069451083 84 0 0 1 0 0 0 45821.26627 -45810.166273 2098571334 4127.042 3660709 0.008116 Apr 2007 10.1 2.3125354238 85 0 0 0 1 0 0 21247.708 -21237.608001 451035993.59 2102.733 9842543 0.014116 May 2007 11.3 2.4248027257 86 0 0 0 0 1 0 31697.85556 -31686.555564 1004037803 2804.12 3090931 0.001958 June 2007 10.8 2.3795461341 87 0 0 0 0 0 1 19877.37925 -19866.57925 394680971.11 1839.498 468118.7 0.010374 July 2007 9.7 2.2721258855 88 0 0 0 0 0 0 7398.973868 -7389.2738677 54601368.291 761.7808 619274.5 0.008609 Aug 2007 8.8 2.1747517215 89 0 0 0 0 0 0 7642.117902 -7633.3179023 58267542.198 867.4225 802826.6 0.002066 Sept 2007 8.4 2.1282317058 90 0 0 0 0 0 0 7893.252102 -7884.852102 62170892.67 938.6729 940100.9 0.001276 Oct 2007 8.1 2.0918640617 91 0 0 0 0 0 0 8152.639038 -8144.5390382 66333516.145 1005.499 1078508 0.00381 Nov 2007 8.6 2.1517622033 92 0 0 0 0 0 0 8420.549911 -8411.9499113 70760901.311 978.1337 1020468 0.01636 Dec 2007 9.7 2.2721258855 93 0 0 0 0 0 0 8697.264834 -8687.5648337 75473782.74 895.6252 6722289 0.003826 Jan 2008 10.3 2.3321438952 94 1 0 0 0 0 0 25159.85702 -25149.557022 632500218.38 2441.705 11422702 0.000848 Feb 2008 10.6 2.3608540011 95 0 1 0 0 0 0 34822.01317 -34811.413166 1211834487 3284.096 40587848 0.000801 Mar 2008 10.9 2.3887627892 96 0 0 1 0 0 0 67542.00827 -67531.10827 4560450584 6195.515 8250808 0.0021042 Apr 2008 10.4 2.3418058061 97 0 0 0 1 0 0 31319.79943 -31309.399434 980278492.92 3010.519 20173961 0.013314 May 2008 11.6 2.4510050981 98 0 0 0 0 1 0 46723.65032 -46712.050321 2182015645 4026.901 6375273 0.00602 June 2008 10.7 2.3702437415 99 0 0 0 0 0 1 29299.89114 -29289.19114 857856717.66 2737.308 1037128 0.012578 July 2008 9.5 2.2512917986 100 0 0 0 0 0 0 10906.32352 -10896.823522 118740762.87 1147.034 1403832 0.005429 Aug 2008 8.8 2.1747517215 101 0 0 0 0 0 0 11264.72559 -11255.925586 126695860.79 1279.082 1745403 0.000129 Sept 2008 8.9 2.1860512767 102 0 0 0 0 0 0 11634.90541 -11626.005408 135164001.74 1306.293 1820635 0.003156 Oct 2008 8.4 2.1282317058 103 0 0 0 0 0 0 12017.25003 -12008.850027 144212479 1429.625 2180741 0.00907 Nov 2008 7.6 2.0281482473 104 0 0 0 0 0 0 12412.1592 -12404.5592 153873089 1632.179 2841818 0.006233 Dec 2008 8.2 2.1041341543 105 0 0 0 0 0 0 12820.04582 -12811.845824 164143393.41 1562.42 Jan 2009 106 1 0 0 0 0 0 37086.4319 Feb 2009 107 0 1 0 0 0 0 51328.75829 Mar 2009 108 0 0 1 0 0 0 99559.07491 Apr 2009 109 0 0 0 1 0 0 46166.38353 May 2009 110 0 0 0 0 1 0 68872.15114 June 2009 111 0 0 0 0 0 1 43188.97426 Dependent Y Variable 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 106 0 2 4 6 8 10 12 14 Chart Title Production Linear Regression for Production 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 103 0 0.5 1 1.5 2 2.5 3 Chart Title Dependent Y Variable lnProduction Linear Regression for Dependent Y Variable lnProduction 1 13 25 37 49 61 73 85 97 5 9 17 21 29 33 41 45 53 57 65 69 77 81 89 93 101 105 109 0 20000 40000 60000 80000 100000 120000 Chart Title Forecast Linear Regression for Forecast
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