There is no equation for locating the median, instead the Median calculation is as follows: 1 . Arrange the data in ascending order from lowest value to highest value. 2. Select the middle observation. If the number of observations is odd, the median is the middle data value, whereas if the number of observations is even, the maiden is the average of the two middle values. As both sets of data have skewed distribution (see 2. 4, Figure 2 & 3), the use of median and mean is advantageous due to its freedom from distortion, which increases the validity and reliability of the central location as a means of analysis.
The central location found through median for the I-J is 2. 8% and 3. 2% for the USA. These figures are close to the central locations found through using mean, this shows me that once again the averages for the % difference in GAP levels annually are both around the targeted 2%. Much like the mean, this figure alone is good for analyzing whether or not the two economies have achieved the economic target of sustainable growth, but cannot show whether or not the two countries are interdependent without more supporting analysis. 2. - Histograms This equal width histogram for the UK is showing the % of which the economy for the I-J has either grown or shrunk over a period of 30 years, compared with the frequency for which that % growth or shrinkage has occurred. The base of each rectangle (% change) is the same throughout the histogram, and that the height represents the class frequency. So as a result, the areas of the rectangles are in reapportion to the respective class frequencies, knowing this, I can see that the bulk of the frequency distribution is the right of the histogram.
This shows that more often than not, the I-J experienced growth % rates between 2-3 %. The Auk's histogram is negatively skewed, meaning that the distribution of the data around the central location found through the mean is dispersed more to the left, in other words, the tail of the distribution curve falls to the left which represents the side of the distribution with fewest observations. The arithmetic mean will be most affected by a few extreme values. Because the I-J is skewed to the left, this shows that the calculated mean is affected by the lower values presented in the 30 year period.
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This equal width histogram for the USA is showing the % of which the economy for the UK has either grown or shrunk over a period of 30 years, compared with the frequency for which that % growth or shrinkage has occurred. Unlike the I-J the, Aqua's distribution is less skewed. Instead we can see that the majority of the Use's data in centralized, with the most frequent figures of % growth in their economy being between 2-4%, also the USA has experienced higher levels of growth wrought the 30 year time p, once experiencing 7%, a level of growth that the I-J never achieved.
The Aqua's histogram is negatively skewed, meaning that the distribution of the data around the central location found through the mean is dispersed more to the left , however, it is less skewed than the I-J, meaning that the figures are higher in value, so that they have less of an impact on the arithmetic mean. This perhaps suggests that the UK and USA are again not as interdependent as their similar mean figures may suggest, because Aqua's figures remained almost normally distributed, whilst the Auk's was significantly more skewed. Furthermore, the USA did not go into recessionary figures as often as the I-J.
These figures suggest that the levels of interdependence do not subsist. However, because using histograms cannot provide a time line of data, they alone cannot show that the two countries experienced the increased or decreased % change in its GAP levels, thus making it impossible to conclude that levels of interdependence do not exist. 2. 5 - The Range More analysis is needed to see if one country's economic fluctuations has a direct impact on another's. As well as measures of central tendency, it's useful to have a assure of the extent of dispersion around that average.
One measure of dispersion is Range, this is the simplest measure of dispersion. To calculate, take the absolute difference between the highest and lowest value of the raw data. While the range is very easy to calculate, It does not provide any quail dative intimation on the dispersion of the values between the two end points. For that reason, knowing the range for each economy in question and seen in figure 2 does not help provide any information regarding the interdependence of the two economies. 2. 6 - Simple Linear Regression
Regression analysis is a useful analytical tool as it involves establishing a relationship between two or more variables, in this case it will be used to establish a relationship between the USA and the Auk's GAP figures, or to show if there even is a relationship. The equation for simple linear regression is as follows:. Broken down this means: Is the dependent or response variable (variable to be modeled). Is the independent or predictor variable (variable used as a predictor of) O = -intercept of the line, that is, the point at which the line intercepts or cuts through the y-axis. = slope of the nine, that is, the change (amount of increase or decrease) in the deterministic component of y for every I-unit increase in . I used simple linear regression analysis to determine if there is a positive association between the Use's GAP figures and the Auk's GAP figures. I decided to see if the Aqua's affected the Auk's because the USA in previous data analysis has proven to be the stronger economy. This has been proved through its higher mean, median and the less skewed positioning of its GAP figures on the histogram (Figure 3).
My own assumption is that If the Aqua's figures go higher, then the Auk's will follow, I believe hat this could be due to levels of interdependence, however it could also be higher levels of the Auk's dependence on the success of the Aqua's economy. When analyzing the data, the dependent variable is the Aqua's GAP figures as I wanted to predict the Auk's potential levels of GAP based on the Aqua's. So the variable being predicted is the dependent variable (I-J) and the variable that's being the predictor is the independent variable (USA).
When choosing what outputs I wanted in the Analysis, I chose estimates, confidence intervals, model fit and descriptive statistics. When looking at plots, I included the histogram of the residuals which are the residuals associated with the dependent variable (I-J) and also the normal probability plot. I also included the Z predictor variable as and the Z residual variable as . This will create a scatter plot. Descriptive Statistics Figure 4 1 . 78675 time p.
This is expected as in a well economically developed country it's expected that economic indicators such as steady GAP growth of 2% would be regularly achieved resulting in the low levels of variance. Correlations Figure 5 Pearson Correlation 1. 000 . 592 This shows that perhaps there is a correlation between the two country's GAP levels, but again, does not sure whether or not there is any interdependence between the two economies or if perhaps one economy is more dependent than the other is, in this case, whether or not the I-J is more reliant on the success of the USA than the USA is of the I-J.
Figure 6 Model R Square Model Summary b Adjusted R Square Stud. Error of the Estimate . AAA . 350 . 327 1 . 46609 a. Predictors: (Constant), USA b. Dependent Variable: I-J In this model summary, the R figure represents the person correlation figure seen in figure 6. Whereas the R square figure shows that 35. 0% of the variability in the Auk's GAP figures can be accounted for by the Aqua's GAP figures. So only 35% of the Auk's GAP change is accounted for by the Aqua's, which isn't much, so whilst it is a meaningful predictor, it isn't accounting for very much.
The standard error of the estimate snows now much error there is in predicting the values shown in texture 6, as seen in the model summary the Stud. Error of the estimate is low, which helps in increasing the validity and reliability of the data. Figure 7 as seen on the left is showing how the variables lie around the regression nine, given that the sample only contains 30 variables, this dispersion of the variables around the line of regression is fairly good, but does not tell me whether or not there are direct or indirect levels of interdependence. . 1 - Time series analysis (Cyclical) - Line Graph The Line graph below shows all 30 years of annual percentage change in GAP plotted for both the I-J and the USA. This graph is an example of a cyclical component of a time series analysis. It's defined as long term variations in time series data that repeat in a reasonably systematic way over time. In this case, it's looking at two equines cycles simultaneously. This graph shows the % change In the Y axis, and the years of the 30 year time period along the X Axis.
Figure 8, as shown to the left, supports the theory of this cyclical component being a business cycle, as the lines fluctuate showing periods of economic boom and recession. This cyclical component of time series analysis is a more diagrammatically demonstration of seeing if the fluctuation of one country's economy has any influence over another's. From a glance it appears that both economies move in similar patterns across 30 years, both peak and fall around the same points along the time line.
However, the UK never reaches the highs that the USA achieves, and for the majority of the time, the US growth per year is slightly higher than that of the I-J. This suggests that whilst potential levels of interdependence being demonstrated in this diagram can't be ignored, it could be argued that the two country's aren't dependent on one another, instead it could be suggested that the UK is dependent on the success of the USA more than the USA is dependent on the success of the I-J. This however is only based on the analysis of a single economic indicator, and more sets of data would be needed in order to purport that statement.
However, the timeline does support the fact that both countries were experiencing normal economic cycles during the 30 year period. 4. 1 Conclusion The data analysis compiled in this report hasn't necessarily proved that there is interdependence between the I-J and the US in terms of each relying on the success of the other's economy, in order for them to achieve their own economic targets and favorable indicator figures. However, it also has not disproved this theory either. All analysis proved that both the I-J and the USA were achieving their economic targets or GAP levels and thus economic growth.
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