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# Correlation and Regression - Essay Example

Summary
The statement “Cigarette Smokers Make Lower Grades than Nonsmokers” reflects a certain relationship between the two activities which are smoking cigarettes and making grades. Therefore, statistically both these activities can be denoted as the two variables i.e. smoking cigarette is one variable and making grades is another variable…

## Extract of sample "Correlation and Regression"

Correlation and Regression Question The ment “Cigarette Smokers Make Lower Grades than Nonsmokers” reflects a certain relationship between the two activities which are smoking cigarettes and making grades. Therefore, statistically both these activities can be denoted as the two variables i.e. smoking cigarette is one variable and making grades is another variable. By looking at the statement, there seems to be identified a very clear and obvious relationship between cigarette smoking and making grades such that high cigarette smoking leads to lower grades and vice versa. From this, it can be observed that if cigarette smoking is increased, it will result in lower grades and if cigarette smoking is decreased, it will result in higher grades, thus effectively identifying a negative or inverse relationship between the two activities that can be estimated. Under statistical terms, the correlation (association) between cigarette smoking and making grades is found to be negative as the both the variables are found to be acting in the opposite directions.
Another important aspect which can be observed from the above statement is that it is actually the cigarette smoking activity that drives the grade making activity. In other words, level of smoking cigarettes determine the grades obtained by the students which means that the there is an impact of smoking cigarettes on making grades or smoking cigarettes causes making grades. In this way smoking cigarettes can be called as the predictor, estimator, explanatory or independent variable, whereas making grades which is the resultant variable can be called dependent variable. On graph, an inverse and linear line can be drawn for predicting this relationship between the two variables.
Question 2
The fact that longer the time patient is taking drug X, the shorter is size of the tumor depicts the relationship between these two variables. It describes the association or correlation that is found between time on taking drug X and size of the tumor such that both of these variables have a relationship with each other. However, this relationship is not so much strong because of the relatively lower value of coefficient correlation which is 0.21. Since the relationship is formulated in such a manner that if patients taking longer time drug X, their tumor is found to be smaller in size which denotes the inverse or negative relationship between the two variables. Graph of these two variables would have more widely scatter dots which represents the weaker association between the two variables.
The other way of using correlation coefficient of 0.21 can be understood by using coefficient of determination which is r2. For this problem, the coefficient of determination is found to be 0.041. Coefficient of determination denotes that the power of independent variable to explain the variability found in the dependent variable. It can be observed here that independent variable is time on taking drug X can only explain 4.41% variability in the size of tumor which is in fact very low. Thus, the strength of relationship between the two variables is found to be very low as both the coefficient of correlation and coefficient of determination for both of these variables are too small to show any strong association between the two variables
References
Gravetter, F., and Wallnau, L. (2008).Statistics for the Behavioral Sciences. Belmont, CA: Cengage Learning.
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