STAT6003 Statistics For Financial Decisions

Descriptive statistics of Industria indicates that it has average sales $17372234 with standard deviation $3333001. The standard deviation is significantly large. It indicates a major variation of the observations from sample mean. The highest sales is $23103581 with a total amount of sale $4.34E+08. The distribution of Sales of Industria is slightly negatively skewed and almost close to normal as the skewness is (-0.05202).

Initial descriptive statistics indicates that Nokaragua has average sales $7859678.624 with standard deviation $97.972. It indicates a minor variation of the observations from sample mean. The highest sales is $85162753.74 with a total amount of sale $196491965.6. The distribution of Sales of Nokaragua is slightly positively skewed and almost close to normal as the skewness is (0.01944256).

Sales data is not present in case of Sweden. However, GDP and Price Index provides a clear approach.

Initial descriptive statistics indicates that Federal Islands has average sales $713603.3679 with standard deviation $177419.6721. It indicates a minor variation of the observations from sample mean. The highest sales is $957950.0905 with a total amount of sale $17840084.2. The distribution of Sales of Nokaragua is positively skewed and close to normal as the skewness is (0.33096273).

The trend of sales of Industria is rising with the presence of some fluctuations in the 25 years. Sales figure for Nokaragua indicates upward trend but sales is lower in amount than Industria. Federal Island indicates a stable and flat trend with the lowest sales figure. Industria has significantly higher average sales over the years from 1991 to 2015.

GDP:

Sweden has highest GDP followed by Industria. GDP is growing over the years and the differences in the GDP are reducing year by year. Federal Island has lagged behind Industria and Nokaragua. Average GDP is also low and insignificant in case of Federal Islands. Sweden has average GDP. Federal Islands has very less amount of average GDP than other countries.

Industrial Population (15-65):

Population trend is higher than other nations in case of Sweden. Nokaragua and Federal Island indicates more or less stable trend. Population of Industria of the range 15-65 years have grown gradually from 1991 to 2009, then got stable after 2009. Federal Island has lowest population in that age limit. Average population (15-65) is insignificant in case of Federal Islands (King’oriah, 2004).

Price Index:-

Federal Islands have significantly different and higher Price Index. Sweden and Nokaragua have similar Price Indexes over the years. Industria has lesser price index than federal Islands. All the Price Index curves of different countries have shown visible fluctuation over the years from 1991 to 2015.

(Rodgers and Nicewander 1988)

• Strong positive correlation is between advertisement and sales (0.986236917) (Miller 2014).
• Strong positive correlation is between sales and number of stores (0.971109284).
• Strong positive correlation is between advertisement and number of stores (0.970966786).
• Survey score has a moderate positive correlation with sales (0.588601019).
• Survey score has a moderate positive correlation with advertisement (0.54833082).
• Survey score has a moderate positive correlation with stores (0.52890297).

• “Sales” has a strong positive correlation with advertisement (0.912745) and stores (0.916224).
• Strong positive correlation is between advertisement and stores (0.969905466).
• Weak negative correlation of survey score exist with sales (-0.20067), advertisement (-0.20232024) and stores (-0.230785592).

• Strong positive correlation is between advertisement and sales (0.990967665).
• Strong positive correlation is between sales and number of stores (0.990458823).
• Strong positive correlation is between advertisement and number of stores (0.992123908).
• Weak negative correlation of survey score exist with all other variables such as with sales (0.019299902), advertisement (0.002906977) and scores (0.011010721).

We are interested to determine whether there is any linear relationship between prices and sales in the three countries except Sweden or not. For determining this, the researcher performed simple linear regression to establish whether there exist any causal relationship between price and sales or not. Prudentially we have to determine the causal relationship assuming the Price factors as independent variable and amount of sales as dependent variables. The relationship was significant to make inference of the total sales (Seber and lee 2012). The level of significance was used as 5% (0.05). The value of multiple R-square is also known as coefficient of determination (Harrell 2015).

The structure of hypothesis is given by-

Null Hypothesis (H₀): There is no significant linear relationship between sales and price factors.

Alternative Hypothesis (H_A): There is a significant linear relationship between sales and price factors.

Multiple R-square = 0.99999 – It indicates a strong linear association of Sales as response and rest other factors as predictors. 99.99% variability  of sales is explained by rest other price factors in Federal Islands.

F-statistic= 198889.0975– The value of F-statistic is high.

P-value=2.22272E-42– p-value less than 0.05 indicates that we can reject the null hypothesis of insignificant association among the factors to predict sales in Federal Islands at 95% confidence interval.

Regression equation to predict sales for the country Federal Islands is

Ln(Sales) = 12.76 + (0.02 * ln(GDP)) – (0.15 * ln(Price Index)) – (0.84 * ln(Population)) + (0.12 * ln(Survey Score)) + (0.63 * ln(Advertisement))  + (0.006 * ln(number of stores)).

Multiple R-square = 0.999992

F-statistic= 198889.0975

P-value=2.22272E-42.

Multiple R-square=0.99999 – It indicates a strong linear association of Sales as response and rest other factors as predictors. 99.99% variability  of sales is explained by rest other price factors  in Industria.

F-statistic=1729984 – The value of F-statistic is very high.

P-value=7.8E-51 –  p-value less than 0.05 indicates that we can reject the null hypothesis of insignificant association among the factors to predict sales in Industria at 95% confidence interval.

Regression equation to predict sales for the country Industria is

Ln(Sales) = 8.40 + (0.02 * ln(GDP)) – (0.26 * ln(Price Index)) + (0.83 * ln(Population)) + (0.17 * ln(Survey Score)) + (0.51 * ln(Advertisement))  + (0.45 * ln(number of stores)).

Multiple R-square=0.99999

F-statistic=1729984

P-value=7.8E-51

Multiple R-square= 0.999999 – It indicates a strong linear association of Sales as response and rest other factors as predictors. 99.99% variability  of sales is explained by rest other price factors in Nokaragua country.

F-statistic= 7801760 – the value of F-statistic is very high.

P-value= 1.01E-56 –  p-value less than 0.05 indicates that we can reject the null hypothesis of insignificant association among the factors to predict sales in Nokaragua at 95% confidence interval.

Regression equation to predict sales for the country Nokaragus is

Ln(Sales) = -5.98 + (0.23 * ln(GDP)) – (0.03 * ln(Price Index)) + (0.48 * ln(Population)) + (0.14 * ln(Survey Score)) + (0.36 * ln(Advertisement))  + (0.31 * ln(number of stores)).

Multiple R-square= 0.999999

F-statistic= 7801760

P-value= 1.01E-56

Note that, the predicted sales values for different years are estimated by taking antilog (Exponential function) of the values from the above equations. As in case of Sweden the values of predictor to predict Sales are not present, we are going to take only Price index and Population 15-65 into account.

Regression equation to predict sales for the country Sweden is

Ln(Sales) = – (0.20 * ln(Price Index)) + (1.70 * ln(Population)).

The average value of the Price Index of consumers is 5.31 for Federal Islands, 2.46 for Industria, 2.04 for Nokaragua and 2.14 for Sweden. We can observe that the price index for Nokaragua is closest to Sweden. The averages GDP for 25 years are 1.3403E+11 for Industria, 222890200.4 for Nikaragua, 1.7188E+11 for Federal Island and 2.89924E+11 for Sweden. Therefore, from this angle also Nokaragua is closest to Sweden. The average population of 25 years in Industria is 2666184, 3565573 in Nokaragua, 5983560 in Sweden and 12514 in Federal Island. Therefore, from this angle too Nokaragua is closest to Sweden. We can interpret that Nokaragua could be the best replacement of Sweden. Forecasted values of parameters of Sweden are given below-

The alternative forecasting techniques that can be applied are trend analysis and exponential smoothing.

Trend analysis is a common forecasting technique used by business or other organization to predict the future outcome based on previous data. In statistics, trend analysis captures the pattern of time series behaviour. Regression analysis provides a cause and effect relation based on least square measures (Cameron &Trivedi 2013). Trend analysis can predict the future values without the estimated equation. It analyse the behaviour of variables overtime and then predict the future value. In this study trend of sales and the dependent variables from 1991 to 2015 and the forecasted value of these indicators are used to predict sales of 2016. Accordingly, the predicted sale of 2016 is calculated as 1050012.9. The predicted value of sales by trend analysis is very close to that obtained from the regression analysis.

Exponential smoothing is a kind of moving average used for time series forecasting. The forecasting is done using the following equation

Where

F_t is the forecasted sales of year t

A_t-1 is the actual sales of previous year

F_t-1 is the forecasted sales of the previous year

α is the smoothening constant , 0<α<1

The forecasting is incorporated for a given value of α. As no value of α is given, it is taken as 0.5. This forecasting technique compares the prior forecasting estimate with actual value and use the difference or error to make fresh forecast (Montgomery, Jennings &Kulahci 2015). Here values of baseline variable are used as a medium of forecasting. In the exponential smoothing previous years’ sales value are utilised to forecast sales in 2016. The forecasted value of sales in 2016 is 898035.5.

  Expansion of business is profitable in Nokaragua as the country shows highest trend. Sweden also indicates good results in various aspects. Advertisement and number of stores should be increased and should be decreased to the decrement of sales. A company in federal Islands should work on all considered factors to grow sales as it indicates comparatively bad results. In Federal Islands, companies need to keep prices low to enhance the amount of sales. In addition, entering a new market in Sweden is Profitable as it shows development almost in all parameters of finance. All the chosen explanatory variables are likely to have large influence on sales.

• The improvement of Federal Islands is required almost in every field.
• Industria need to emphasize on GDP US$ and price factors such as survey score and number of stores.
• Variation in sale amount of all the countries are needed except Sweden.
• Number of stores is to be increased in comparatively backward countries like Federal Islands or Industria.

Cameron, A. C., &Trivedi, P. K. (2013). Regression analysis of count data (Vol. 53). Cambridge university press.

Harrell,F.E. (2015). Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Cham: Springer.

King’oriah, G. K. (2004). Fundamentals of applied statistics. Nairobi: The Jomo Kenyatta Foundation.

Miller, A. (2014). Application of Excel® Pivot Tables and Pivot Charts for Efficient Library Data Analysis and Illustration. Journal Of Library Administration, 54(3), 169-186. https://dx.doi.org/10.1080/01930826.2014.915162

Rodgers, J. L., & Nicewander, W. A. (1988). Thirteen Ways to Look at the Correlation Coefficient. The American Statistician, 42(1), 59–66. Retrieved from https://www.stat.berkeley.edu/users/rabbee/correlation.pdf

Seber, G.A., & Lee, A.J. (2012). Linear regression analysis. New York: Wiley