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DESCRIPTIVE STATISTICS & REGRESSION ANALYSIS 11

Descriptive Statistics & Regression Analysis

Introduction

The relationship between one or more variables and other variables are best determined from statistical viewpoint. Using Statistical description therefore one of the sure method of illustrating the links in social, economic, scientific, psychological, and other life-related variables. This report therefore sought to determine the relationship between the stated phenomena like Gouldian Finch body characteristics, and the analysis of the weight of the Tasmanian devil’s weight and height.

The method adopted for the study involved utilizing the qualitative and quantitative research techniques in reviewing the given data on the topic. Using statistical tools of analysis such as SPSS, the relationship between different variables as stated above are acutely analyzed.

Analysis 1: The difference between the total length of the Gouldian Finch and its wingspan

The Gouldian Finch is a small colorful Australian bird currently believed to be endangered due to habitat loss and extreme weather conditions. Out of the 136 Gouldian Finch examined, the analysis below shows the difference between thetotal length of the Gouldian Finch and its wingspan.

Hypothesis; the Gouldian Finch has a wingspan which is equal, on average, to its length

Descriptive Statistics: length, wingspan, difference

Variable N Mean StDev

Length 136 159.87 3.99

Wingspan 136 244.61 5.69

Difference 136 84.738 6.80

Out of the 136 examined Gouldian Finch; the mean length was 159.87 with a standard deviation of 3.99. The wingspan on the other hand had a mean of 244.61 with a standard deviation of 5.69. Finally, the difference between the two was averaged at 84.738 while the standard deviation of the difference was 6.80. From the analysis therefore, it means the null hypothesis is rejected, meaning that the Gouldian Finch do not have a wingspan which is equal, on average, to its length. The same can also be supported by the graph below that shows that wingspan (260-230=30) is not equal to its average length (175-150=25).

Based on the frequency visa-a-vie length, the peak length is approximately 28 while that of the peak wingspan is approximately 32 as shown in the graph 2 and 3 below.

Graph 3

The graph of the difference between the mean and the standard deviation of the length and wingspan of Gouldian Finch is best illustrated in the graph below. The peak point of the difference between the two is 23.

Analysis 2: Tasmanian Devils in Cradle Mountain

The main purpose of this analysis was to determine the relationship between the weights of Tasmanian Devils and their lengths, head lengths and heights, respectively.

In an x-y diagram as shown below, the scatter diagram helps to determine the relationship that exist between two variables. The more the two data sets agree, the more the scatters tend to concentrate in the vicinity of the identity line; if the two data sets are numerically identical, the scatters fall on the identity line exactly.

The scatter plots above represent the relations between the weights of Tasmanian Devils and their lengths, head lengths and heights, respectively.

According to the graphs above, the scatter diagram of graph 5 best predicts the Tasmanian Devil’s overall weight. Graph five has sets of data that agree and the scatters tend to concentrate in the vicinity of the identity line making it more predictive than the other scatter diagrams.

b. As argued by Blank (2008), an outlier is an extremely high or low value when compared to the rest of the values in range of data. Largest residual in each scatter is 120 and is actually not part of the same Tasmanian Devil since it has a larger deviation from the range and mean of the data obtained from Tasmanian Devil.

c. After the removal of the outlier, the output above relates to the relation between length and weight.

Regression Analysis: weight versus length

The regression equation is

Weight = — 5.66 + 0.214 length

Predictor Coef SECoef T P

Constant -5.662 1.571 -3.60 0.000

Length 0.21391 0.02144 9.98 0.000

S = 0.369915 R-Sq = 42.6% R-Sq (adj) = 42.2%

Graph 8

From the descriptive diagrams above, it is pretty clear that the gradient is negative, i.e. — 5.66. This means that the heaviest Tasmanian Devil not also the longest but the reverse is true.

d. The approximate length of the Tasmanian Devil with the lightest weight is 71.8

1. The Tasmanian Devil with the largest residual in the plot above weighed 9.0kg and was 73.1cm long. Circle this observation on the plot. Calculate the value of the residual.

The length is 73.1cm=0.731m

Weight is 9kg=9000g

Residual value =9000/0.731

=12311.9

Regression Analysis: weight versus height

In analyzing the link between weight and height, the following regression analysis was found.

The regression equation is

weight = — 13.4 + 0.733 height

Predictor Coef SECoef T P

Constant -13.45 13.67 -0.98 0.327

height 0.7331 0.4272 * *

S = 0.483111 R-Sq = 2.2% R-Sq(adj) = 1.4%

The adjusted R-squared is a positive number indicating the extent to which weight and height have a strong relationship. The graphs below indicate the relationship between height and weight, that as weight increases, weight also increases.

Graph of weight and height

Considering the shape of the curves, and also the positive 1.4 R-squared from the descriptive statistics, it is logical to state that height is a useful predictor of the weight of Tasmanian Devils.

References

Blank, S. S. 2008. Descriptive statistics. New York, NY, Appleton-Century-Crofts.

Johnson, R., & Kuby, P. 2012. Elementary statistics. Boston, Brooks/Cole, Cengage Learning.