The quarterly data for sales of a series of mountain bikes by a manufacturer for
ID: 3176236 • Letter: T
Question
The quarterly data for sales of a series of mountain bikes by a manufacturer for the post four years are shown in the tale below:
Years
Quarters
Sales (units)
2013
1
1,280
2
1,350
3
1,770
4
1,880
2014
1
1,420
2
1,520
3
1,820
4
1,930
2015
1
1,450
2
1670
3
1,900
4
2,000
2016
1
1,710
2
1,770
3
2,190
4
2,210
a.
Compute the corresponding seasonal (quarterly) indexes (to an accuracy of four decimal places) by comparing the original time series data with their respective centered moving averages (use the median to remove irregular variations to get the adjusted seasonal indexes). Briefly comment on the second and third seasonal indexes obtained.
b.
Determine the linear trend of the sales of mountain bikes by fitting a linear regression line to the given sales figures with the time period. Then use the linear trend, together with the seasonal index obtained in part (a), to forecast the sales figures of mountain bikes for the four quarters of the year 2017.
Years
Quarters
Sales (units)
2013
1
1,280
2
1,350
3
1,770
4
1,880
2014
1
1,420
2
1,520
3
1,820
4
1,930
2015
1
1,450
2
1670
3
1,900
4
2,000
2016
1
1,710
2
1,770
3
2,190
4
2,210
Explanation / Answer
Second Quarter have less than 90, and there is a sudden jump in quarter 3 to 110
b) Sample size: 16
Intercept (a): 1387.25
Slope (b): 41.720588235294
Regression line equation:
y=1387.25 + 41.720588235294x
where X is quarter no from starting
eg . q3 of 2014 is X = 7
Now regression line for X and ynew
Y new = 1478.7266172 + 30.958633277941x
Years Q1 Q2 Q3 Q4 Annual avg 2013 1280 1350 1770 1880 1570 2014 1420 1520 1820 1930 1672.5 2015 1450 1670 1900 2000 1755 2016 1710 1770 2190 2210 1970 average Q 1465 1577.5 1920 2005 1741.875 Q/yr 84.1047722 90.5633297 110.22605 115.105849 100Related Questions
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