correlation between weigh and age

Correlation between age and weight
Name
Institutional affiliation
Correlation between age and weight
Several studies such as epidemiological studies give special regard to age and weight since the variables act as both confounding variables and primary exposure variables. This paper aims at discussing the statistical ways of analyzing the differences in the two variables (age and weight) using hypothetical data. The paper also interprets the various statistical outputs that are computed from the data.
Null hypothesis: There is no statistical significance between age and weight
Alternative hypothesis: there is a statistical significance relationship between age and weight of bears.
Descriptive statistics.
Assume a hypothetical data set with a mean age of 43.51 years and mean weight of 182.88 kilograms. This data will help to show how differences between the two variables can be analyzed. An excel spreadsheet will be used to obtain the results, and the paper will attempt to give an interpretation of the results. Other useful characteristics of the two variables are described below.
Age Weight
Median 34150
Mode 57166
SD33.72121.80
Variance 1137.08714835.53
Differences in variables such as height and weight can be analyzed by using various methods such as correlation coefficients and independent t tests.
Correlation refers to the degree of association between two different variables (Ross, 2004). The degree of association is expressed by the correlation coefficient which takes values ranging from +1 and -1.

When the correlation coefficient (r) is negative, it means that one variable (either x or y) tends to decrease as the other variable increases implying that there is a negative correlation or reveres relationship between the two variables. Conversely, in situations where the correlation coefficient (r) is positive, it means that an increase in one variable leads to an increase in the other variable i.e. there is a direct relationship (association) between the variables under consideration. The correlation coefficient is higher as its value gets close to positive one (+1) or negative one (-1), and is getting smaller and smaller as it gets close to zero. The computation of the correlation coefficient begins with the computation of the covariance of the variables.
The relationship between variables can also be plotted on a scatter diagram as shown below. Variables that have little variance will always have a linear line with few or no outliers while those that have differences will have several outliers.

The x-axis represents the age of the variables while the y-axis represents the weight of the variables.
From the above graph, it is easy to spot that there are major differences between the age variable and the weight variable. The graph comprises several outliers that give an insight of how different the two variables are. The degree of these differences cannot, however, be determined by a mere representation of the graph and therefore advanced statistical methods of difference analysis ought to be employed. However, if the Pearson’s correlation value is computed, different results will be obtained because of the strength of the measuring tool. For instance, using the same data as the one that was used to obtain the results above, the correlation coefficient of 0.749013 is obtained. This can be interpreted to mean that there is a strong association or relationship (few differences) between the two variables that are under consideration.
Inferential statistics.
Independent t-test.
This group of statistics comes in handy in the examination of differences between two quantitative or numerical variables. In determining the variances between variables, the independent t tests makes assumptions such as the equality of the variances of the variables.
In the difference analysis of age and weight, we can assume that the means are equal then use the independent t-test to verify the claim.
Using the hypothetical data (attached in excel), the following output can be obtained from excel spreadsheet. 95 percent confidence level has been assumed.
Null hypothesis H0: var1=var2
Alternative hypothesis H1: var1~=var2
t-Test: Two-Sample Assuming Equal Variances   Variable 1 Variable 2
Mean 43.51851852 182.8888889
Variance 1137.084556 14835.53459
Observations 54 Pooled Variance 7986.309574 Hypothesized Mean Difference 0 df 106 t Stat -8.103623699 P(T<=t) one-tail 4.92277E-13 t Critical one-tail 1.659356034 P(T<=t) two-tail 9.84554E-13 t Critical two-tail 1.982597262  
From the output, p-value for the two-tailed sample t-test is 4.922. Since the p>0.05, the results of the study show that there is a big difference between the variances of the two variables. We, therefore, fail to accept the null hypothesis and fail to reject the alternative hypothesis.
Since both the occurrences of p have a value that is greater than 5 Percent, one can make a conclusion that there are significant differences between age and weight of the variables.
In conclusion, weight will always vary depending on the age of the bears. Older bears will tend to have more weight relative with those of younger bears. This is because they are fully developed and have mastered their feeding habits and also the ecosystems that have plenty food. Additionally, the sexuality of the bears will also influence the weight of the bears regardless of their ages.
References
Brase, C. & Brase, C. (2009). Understandable statistics (1st ed.). Boston, Mass.: BrooksCole.
Ross, S. (2004). Introduction to probability and statistics for engineers and scientists (1st ed.). Amsterdam: Elsevier/Academic Press.

.