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The total number of overtime hours (in 1000s) worked in a steel mill was recorded for 16 quarters, as shown below.

 Year Quarter Overtime hours 2013 1 20 2 30 3 28 4 20 2014 1 24 2 34 3 28 4 21 2015 1 28 2 38 3 31 4 26 2016 1 30 2 41 3 35 4 28

Use the regression technique to calculate the linear trend line.

1. Calculate the seasonal indexes based on the regression trend line in part (a).

2. Write a report of on business decisions to be made on the basis of what seasonal indexes tell us?

## Empirical trends captured through Seasonal Indexes

Using the given data with regards to time and overtime hours, the regression model has been computed with time as the independent variable and overtime hours as the dependent variable.

• The regression equation based on the above output is as highlighted below.

Where y represents overtime hours

1. b) Using the regression line computed above, seasonal indexes need to be computed.  This has been done by adhering to the following steps (Hillier, 2016).
• Step 1: For value of the independent variable t=1 to t=16, the predicted value of y or overtime hours needs to be computed.
• Step 2: Compute y/ypredicted for each of the 16 values which would result in values for the four years across each quarter.
• Step 3: Average for each quarter needs to be taken and suitable adjustment needs to be made so to yield the seasonal indexes.

Hence, based on the above output, seasonal indexes for the Q1, Q2, Q3 and Q4 are 0.9106, 1.2511,1,0462 and 0.7921 respectively.

There are several businesses which have a seasonal trend which implies that sales in a particular seasons or financial quarter may be significantly higher than the other. As a result, the associated costs would also show a seasonal trend.  This is especially the case with businesses which tend to be based on seasons such as products having higher sales in either summers or winters. Further, the hotels also tend to have high seasonality owing to the difference in occupancy levels in the peak and lean season (Hair et. al., 2105). This seasonal variation in the business is often captured through the seasonal trend which represents as to which season would witness high business and which would witness low business owing to the nature of the business. Typically, seasonal indexes in excess of 1 is representative of above average trends while a value of less than 1 would represent lower than average trend (Flick, 2015). In the wake of this background, the objective of this report is to highlight the key role that the seasonal indexes tend to play in the business decision making.

The various spheres of business decision making where seasonal indexes can play a vital role are discussed below.

Businesses are essentially forward looking but the same is done taking the empirical trends into cognizance. These empirical trends are essentially captured through the use of seasonal indexes since it highlights the seasonal trends that are visible in the business. Considering that these seasonal variations are inherent in the business and cannot be dispelled away with, it is imperative to take these into consideration for any future forecasting of the business. It is essential the future trends of business should consider these and capture them in forecasting so that an accurate forecasting can be drawn. This plays a pivotal role in the management decision making (Hastie, Tibshirani and Friedman, 2011).

Consider for instance, an ice-cream manufacturer whose business tends to seasonal with sales in summers being 50% higher than the corresponding sales in winter. Assume that the company is running at 100% capacity utilization and is able to match 100% sales demand in summers. However, owing to the popularity the management estimates that in the future demand is expected to grow further. In such a scenario, it is essential to take into consideration the seasonal indexes so as to be able to forecast the summer sales accurately going ahead. This is because the sales in the winter months would not pose a problem for the company as it already has a spare capacity. Hence, based on incremental unmet demand in the future, the management of the company would need to have suitable arrangements in place so that the business interests are safeguarded (Hillier, 2016).

## Importance in forecasting future trends

The case of the given steel mill can also be taken into consideration. The given data highlights the overtime hours which essentially would be linked to the production of steel. Hence, it would be fair to conclude that in the quarters when the overtime hours are more, the production of steel would be also higher. The seasonal indexes for the Q1, Q2, Q3 and Q4 have been computed as 0.9106, 1.2511,1,0462 and 0.7921 respectively. Based on the above, it can be estimated that steel production is highest in Q2 and is about 25% higher than the average production level. Further, the lowest production of steel would be witnessed in Q4 where the steel production would be 21% lower than the average.  Considering the differential overtime hours in different quarters, it is essential that the manpower planning needs to be carried out using the above information. Additionally, the manpower must also ensure that their availability corresponds to the seasonal trends so that the business demands can be fulfilled (Hair et. al., 2015).

The forecasting using seasonal indexes is also quite helpful in considering the capital projects particularly when the capacity utilisation is very high and hence additional capacities would have to be set to cater to the incremental demand. These decisions cannot be undertaken without the accurate forecasting of the future requirements of the business. Thus, the seasonal indexes play a critical role in ensuring that the business can capitalise on the potential future growth in the most cost efficient manner. Capitalising in the cost efficient manner is essential considering that capacity expansion if often not the right choice considering that surplus demand is limited to particular quarters only and thus the management needs to consider all options particularly outsourcing manufacturing (Flick, 2015).

The presence of seasonal trends can make it difficult to analyse the business as the rise and fall in sales or profits can be attributed to the seasonal factors. Hence, it is essential to deseasonalise the financial information so as to obtain the data which is free from the seasonal effects. This information is easier to interpret and highlight the business trends based on empirical trends. Further, any deviations from a general trend can also be interpreted in seasonal terms.  This is because the positive or negative performance of the business may be attributed to seasonal factors which are external to the business and hence not in the control of the management.  Based on this, the management can assess the performance of not only the business but also the underlying employees (Hastie, Tibshirani and Friedman, 2011).

Conclusion

On the basis of the above, it can be concluded that seasonal indexes provide vital information in relation to the seasonal variation of the business. Further, it is imperative for the management to consider this seasonal trend owing to the pivotal information that is contained which can help not only in forecasting but also analysis of business trends. This information is critical in order to take useful decisions with regards to the future of the business and other decisions regarding capital investment especially for fulfilling the incremental demand expected in the future.

• The relevant inputs required for hypothesis test are highlighted below.

Population standard deviation

Random sample

Average

• In order to conduct the given hypothesis, the following hypotheses need to be taken into consideration.

i.e. the average score on an exam for University of Adelaide does not differ from the national average of 1300.

i.e. the average score on an exam for University of Adelaide is higher than the national average of 1300.

• The value of test statistic needs to be computed.

It can be seen from the above that population standard deviation is given and therefore, the distribution can be assumed to be normally distributed and hence, z statistic would be taken into consideration as the relevant test statistics (Flick, 2015).

The value of z statistic comes out to be 3 and can be represented using the following graph.

• The p value needs to be computed so as to decide if the null hypothesis ought to be rejected or not.

For right tailed hypothesis testing, the p value comes out to be 0.00135.

• Assumed level of significance = 5%

It can be seen from the above analysis that p value is lower than level of significance and therefore, sufficient evidence is present to reject the null hypothesis and to accept the alternative hypothesis. Therefore, the conclusion can be drawn that “average score on LSAT paper at the university of Adelaide is significantly higher than the national average of 1300” (Eriksson and Kovalainen, 2015).

• Probability of type II error

And,

Here, rejection region needs to be determined.

Now,

Therefore, probability of type II error comes out to be 0.3612.

References

Eriksson, P. and Kovalainen, A. (2015) Quantitative methods in business research (3rd ed.). London: Sage Publications.

Flick, U. (2015) Introducing research methodology: A beginner's guide to doing a research project (4th ed.). New York: Sage Publications.

Hair, J. F., Wolfinbarger, M., Money, A. H., Samouel, P., and  Page, M. J. (2015) Essentials of business research methods (2nd ed.). New York: Routledge.

Hastie, T., Tibshirani, R. and Friedman, J. (2011) The Elements of Statistical Learning (4th ed.). New York: Springer Publications.

Hillier, F. (2016) Introduction to Operations Research (6th ed.). New York: McGraw Hill Publications.

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