# Statistics Assignment

• Category:
Statistics
• Document type:
Assignment
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910
 Profit in Billion dollars
 Profit in Billion dollars Inflation Rates %  a) The variable that is used in the x-axis for the first graph is inflation rates and the y-axis represents profits in dollars. The variable used in the x-axis for the second graph is years, and the y-axis represents profits in dollars.

b) The inflation rates are used in the x-axis because it is the independent variable. The profits of the company will most likely depend on the inflation rates and other economic indicators and as such the profits will be taken as the dependent variable (y-axis). The profits of the company can be estimated using the determined regression equation when the inflation rates are known.

The year is used as the independent variable in the second graph. The profits will increase over the years and as such the y-axis will represent the profits because it is the dependent variable in the equation. The profits of the company can be estimated using the determined regression equation for any desired year.

c) The graph indicates that there exists a weak negative correlation between the variable profits and inflation rates. It is expected that as the inflation rates increase the economic conditions of that particular country will be affected. Consequently, the profits that will be gained by the entities in that country will not be that high. The negative correlation observed was expected.

d) The value of an appropriate correlation coefficient is between -1 and 1. 1 signifies a strong positive correlation, -1 a strong negative correlation and 0 signifies no correlation between the variables.

Spearman’sRank correlation coefficient

 Profit in Billion dollars Inflation Rates % D-squared 0 0

Correlation coefficient = 1 – 6(∑ d2)/n(n2 – 1)

=1 – 6(232)/10(102-1)

Pearson’s product correlation coefficient

 Profit in Billion dollars Inflation Rates % Y-squared X- squared

Persons product correlation coefficient = n(∑xy) – (∑x)(∑y) / √ [n∑x2 – (∑x)2][ n∑y2 – (∑y)2]

= 10(99.898) –(27)(37.37)/ √[10(79.32) – (27)2][10(141.4)– (37.37)2]

= -10.01(√(64.2)(17.48)

= -0.2988

e) There is a difference between the correlation coeficients computed with the Pearson product correlation coefficient being slightly less than the Spearman’sRank correlation coefficient. The scatterplot of profits against inflation rates indicated significant outliers. Consequently, Pearson correlation coefficient is not the best correlation coefficient to use because it is sensitive to outliers. The coefficient that is suitable for this analysis is the Spearman’srank correlation coefficient because it does not discriminate on the presence of outliers.

f) The value of the correlation coefficient suggests that not much of the variance in the dependent variable can be explained by the independent variable. The independent variable cannot be a good estimator of the independent variable. Inflation Rate

j) The coefficient of determination gives an estimate of the variance in the dependent variable that could be explained for by the independent variable. Consequently, the higher the value of the coefficient of determination the more reliable the independent variable in predicting the independent variable. The coefficient of determination in this analysis was 0.093. 9.3% of the variance in the dependent variable could be explained for by the independent variable. The small value of the coefficient of determination has the implications that the predictions of the profits are not reliable. The second reason as to why the prediction is not reliable is the failure of the data points in the sample to have a distinct line of best fit.

k) The correlation analysis suggests that there is no significant correlation between the variables profits and inflation rates. A correlation value between 0.8 and 1 is considered to be a strong correlation while that of less than 0.8 is considered to be weak. The regression analysis did not provide a line of best fit, additionally, the coefficient of determination obtained was small which indicates that the regression equation cannot be considered to be reliable enough in predicting the dependent variable. The graphical representation indicates that the expected profits for years 2016 and 2017 is 4.2 and 4.4 billion dollars respectively.

 Profit in Billion dollars Semi totals semi average
1. Method of least squares

The regression equation is y = -0.095x-187.711

Profits for 2016 using the regression equation will be 3.809billion

The profits for the year 2017 will be 3.904

 4.261133333 4.355921212

Using the forecast function in excel, the profits for the years 2016 and 2017 will be 4.2611 and 4.356 billions respectively.

 Profits for 2016 Profits for 2017 Graphical Semi average Least squares Forecast

Comparing the above methods, the technique that is more suited for making the predictions is either the forecast or graphical technique. The range of profits for the company appears to have stabilized in the years 2014 and 2015 at a figure that is more close to that obtained by the two techniques. The forecast technique is chosen to be the most suitable method that can be used to predict the estimate. The regressin analysis did not yield an line that allows most of the data points to pass through it, in fact none of the points in the sample coincided with the line of best fit which gives doubt of the credibility of the line of best fit in being used to estimate future profit values. The estimates that are made using the forecast technique are reliable because an algorithm was applied to the existing data points to provide a close estimate.

Reference List:

BURNS, N., GROVE, S. K., & GRAY, J. (2011). Understanding nursing research building an evidence-based practice. Maryland Heights, MO, Elsevier/Saunders. http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1167270.