AM 5112 Business Statistics and Analysis - Time Series Assignment

This assignment solution focuses on time series analysis and forecasting techniques using sales data from 1997 to 2011. It includes a scatter diagram, regression analysis, and the calculation of the coefficient of determination to assess the goodness of fit. The solution also involves forecasting sales for January 2012 using both regression and exponential smoothing methods, along with an evaluation of the prediction accuracy. Furthermore, the assignment extends to the analysis of quarterly sales data, employing a multiplicative model to account for seasonal fluctuations and trends, with detailed calculations of adjusted seasonal values and forecasting for the year 2019. The reliability of the forecast is assessed using Mean Absolute Percentage Error (MAPE) and a discussion of the model's ability to capture seasonal patterns. The assignment also includes references to relevant literature and an appendix with supporting data and calculations.

Running head: BUSINESS STATISTICS AND ANALYSIS
Business Statistics and Analysis
Name of the Student:
Name of the University:
Author Note:

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BUSINESS STATISTICS AND ANALYSIS
Table of Contents
Section B....................................................................................................................................2
Reference and bibliography.......................................................................................................3

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BUSINESS STATISTICS AND ANALYSIS
Solution 1
Solution 1.a: Scatter Diagram
Figure 1: Scatter diagram of the data set and the trend line
The scatter diagram shows the fluctuation of the sales over time. However, the trend
line is upward rising which indicates that the trend of sales is upward rising.

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BUSINESS STATISTICS AND ANALYSIS
Answer 1.b: Least Squares Regression Line
Figure 2: Least square regression line
Answer 1.c: Coefficient of determination
The coefficient of determination that is adjusted R2 is equal to 0.6724. This shows the
goodness of fit for the regression line. The value indicates that the trend line can predict the
sales value with 67.24% accuracy (Nakagawa, Johnson & Schielzeth, 2017).
Answer 1.d: Prediction of sales
The regression equation Y =84.09∗X+ 34 106
The predicted sales for 2012 is Y =84.09∗16+34106=47563.4
The prediction is 67.24% accurate.

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Answer 1.e: Exponential smoothing to forecast sales.
Figure 3: Exponential forecasting for sales
The predicted sales by exponential smoothing for January 2012 is 43526.
Answer 1.f: Exponential smoothing and Regression forecasting.
Mean absolute percent error for the exponential forecasting is 1.45% and the
regression forecasting is 5.56%. The MAPE for the regression forecasting is high as it does
not consider the previous actual value of the target variable while forecasting and thus it does
not consider the fluctuation. The exponential smoothing considers the previous actual value
with the present one to forecast the future value (Montgomery, Jennings & Kulahci, 2015).
Solution 2
Solution 2.a: Model
The data is a time series data. The scatter plot of the quarterly data shows that there
exist a seasonal fluctuation and the spread of the seasonal fluctuation is increasing over the

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BUSINESS STATISTICS AND ANALYSIS
time. Along these all, the trend is also upward rising. So, to forecast the time series data with
moving average technique, the multiplicative model is best.
Solution 2.b
Figure 4: Quarterly sales for concept corporation products
Solution 2.d: Adjusted S values for each quarter
Table 1: Adjusted S calculation
Adjusted S Calculation
2015 2016 2017 2018 Adjusted SI
1 1.13 1.06 1.07 1.08
2 0.96 0.97 0.96 0.96
3 0.69 0.71 0.73 0.71
4 1.21 1.26 1.24 1.24

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BUSINESS STATISTICS AND ANALYSIS
Solution 2.e: Regression equation and R2
Figure 5: Deseasonalised quarterly sales for concept corporation products
Solution 2.g: Prediction of sales for the year 2019
The regression equation of the trend line is Y =1.8566∗X+96.976
The deseasonaalised sales value of the 1st quarter of 2019 is
Y =1 .8566∗17+96.976=128.54 and the forecasted sales value is 139.41.
The deseasonaalised sales value of the 2nd quarter of 2019 is
Y =1 .8566∗18+96.976=130.39 and the forecasted sales value is 125.40.
The deseasonaalised sales value of the 3rd quarter of 2019 is
Y =1 .8566∗19+96.976=132.25 and the forecasted sales value is 93.40.
The deseasonaalised sales value of the 4th quarter of 2019 is
Y =1 .8566∗20+96.976=134.11 and the forecasted sales value is 165.75.

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BUSINESS STATISTICS AND ANALYSIS
Solution 2.h: Five years of AR
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
50
70
90
110
130
150
170
Quarterly Sales for Concept Corporation Products from
2015 to 2019
Quarter ID
Decentralized AR ($ million)
Solution 2.i: Reliability of the forecast
The MAPE of the forecast is 2.38 which is very low. So, the forecast is reliable
enough. Moreover, the forecast value of the quarters of 2019 captures the seasonal trend. So
the model is reliable to forecast the data (Box et al. 2015).

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BUSINESS STATISTICS AND ANALYSIS
Reference and bibliography
Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis:
forecasting and control. John Wiley & Sons.
Chatfield, C. (2016). The analysis of time series: an introduction. Chapman and Hall/CRC.
Kumar, K., & Raj, M. A. M. (2016). Improving efficacy of library services: ARIMA
modelling for predicting book borrowing for optimizing resource utilization. Library
Philosophy and Practice (e-journal), Paper, 1395.
Montgomery, D. C., Jennings, C. L., & Kulahci, M. (2015). Introduction to time series
analysis and forecasting. John Wiley & Sons.
Nakagawa, S., Johnson, P. C., & Schielzeth, H. (2017). The coefficient of determination R 2
and intra-class correlation coefficient from generalized linear mixed-effects models
revisited and expanded. Journal of the Royal Society Interface, 14(134), 20170213.
Wu, X., Zhu, Z., Su, X., Fan, S., Du, Z., Chang, Y., & Zeng, Q. (2015). A study of single
multiplicative neuron model with nonlinear filters for hourly wind speed
prediction. Energy, 88, 194-201.