BUS107 Quantitative Methods

Question One

Part a

The overall portfolio return for the two business ideas is done to determine which between the two will realize the maximum profit for the bright and gloomy days

For the first option,

The final table is shown below,

Newcrest will opt for option A since it results in higher profits compared to option two for the two-day conditions combined (gloomy and bright).

Part b

A new model that can be used in this case is designed as follows:

Part b

Values

Solver

answer

Question Two

Part a

There are varying number of newborns across the world over time period, for instance days, hours, months or even in years and quarters. Based on this reality, the study sought to investigate the overall trend of children born in Singapore for the period between the first quarter of 1986 and the first quarter of 2020. This was done using an overall trendline as shown in figure 1 below.

Fig 1. Time series trend for Newborn babies in Singapore (1986-2020)

It is clear that a general decline in the number of newborns was experienced in the country. Individually, the highest number of newborns in Singapore was recorded in 1988 the fourth quarter while the least was recorded in the 1^st quarter of 2015. This confirms the seasonality trend displayed by the numbers of time period. This is true as confirmed by the Jon Emont report (2020) which states that there is lower rates of fertility due to unreadiness by some people to give birth and the longer life expectancy which implies that most people have attained their menopause (Emont, 2020).

Part b

Making the prediction for the 2020 quarters three and four, 2021 quarters one, two, three and four involved the use of simple linear regression, an accurate measure for approximating the predictions along a straight line. This method was applicable since the variables were closely aligned to the trend line hence proving a higher sense of accuracy. Using the model, the change in years explained 34.54% of the model variation which can increase when other confounding variables are added to the variables. The overall influence of change in years on the number of newborns was significant, (F (1, 136) =71.77, p<.05). The resulting equation of the regression model is,

The resulting equation of the regression model is,

y=12134.84 - 19.6852x

Using the regression equation and replacing x with the respective values below, prediction was conducted for the desired period as shown in the table below.

Table 2. Prediction table

c: Part C-Sources of Forecasting Error in Social Sciences

Unlike physical sciences, social sciences have experienced a substantial amount of uncertainty in terms of predictions based on the diverse number of successes and failures. This has majorly been attributed to the attitude of extrapolating in a linear fashion from the present to the future and second, to the fear of the unknown alongside the psychological needs for reducing the anxiety associated with such fears by researchers developing a belief that they can control the future (Spyros Makridas, 2020). Let’s take the case of Microsoft CEO who predicted no chance of iPhone getting any market share. He used the past and by then present records to predict the future forgetting that there were to e changes in consumer taste and preference. Besides, he developed an attitude of extrapolating in a linear fashion from the present to the future forgetting the existence of seasonal changes in trends towards the future.

References

Emont, J. (2020, February 22). Singapore Isn’t Kidding When It Comes to Fostering Fertility. Wallstreet Journal. Retrieved from https://www.wsj.com/articles/singapore-isnt-kidding-when-it-comes-to-fostering-fertility-11582376400

Spyros Makridas, R. J. (2020). Forecasting in social settings: The state of the art. International Journal of Forecasting, 15-28. doi:10.1016/j.ijforecast.2019.05.011

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