A regression analysis is a statistical assessment of the association between two

Question

A regression analysis is a statistical assessment of the association between two variables, one of which is dependent and the other, independent. The dependent variable is y and the independent variable is x. Regression analysis is used to find the relationships between these variables. Variables within a regression analysis can be negatively correlated or positively correlated.

A situation in which one could model a regression analysis could be the association of hours studied and a grade on a test. The independent variable in this situation is the hours studied, and the dependent variable is the grade on the test because the grade is dependentthe hours studied. The amount of hours one studies has a direct impact on a grade on a test. The relationship between hours studied and the grade on the test is positive because the more hours one studies, theoretically, the better their grade should be.

Write about a real-life situation from which one could model a regression. Explain the situation in detail, and specifically, the independent variable and dependent variable.

Initial posting should be 250-500 words.

Explanation / Answer

An example of positively correlated Regression:

Consider a real life model of the number of passengers travelling in a metro train on a given day and the revenues collected from ticket vending of metro department. Since the major source of income for the metro department is by selling tickets to commuters, the revenue of the department depends on the number of commuters that use the services of metro. Hence the number of travelers on any given day serves as an independent variable for our model, whereas the revenue collected by the metro department is the dependent variable. The roles of the dependent and the independent variable cannot be interchanged here as the increase in revenues of the metro could also be from some other source like advertising. Thus, the independent variable and the dependent variable are clearly defined with no ambiguity whatsoever. The number of passengers may vary at different times of the day. For example at office hours, people would prefer to commute by metro and hence the revenues at that time would be higher as compared to the revenue collected at any other time. Also on public holidays people might use metro less hence adversely affecting the revenues. The model is positively correlated since an increase in the independent variable also increases the dependent variable i.e., the number of passengers commuting through metro is directly proportional to the revenues earned by the metro department. Thus the revenues will show an increase if the number of commuters is high and the revenues will fall if the commuters are less. The regression thus modeled by the use of these independent and dependent variables will depict a positive correlation.

An example of negatively correlated Regression:

Consider a model encountered in real life relating the health of an individual and the number of visits he/she pays to the hospital. We only consider the ailments which require medical attention by expert doctors and hence require a visit to hospital. Let us not include those diseases in our model which are treated easily at home and do not require a visit to the hospital. Thus health of an individual in this model is only dependent on the number of serious ailments that require medical expertise. Since any individual would be visiting a doctor only if he/she is not feeling well, hence the health of a person is the independent variable and the number of visits to the hospital serves as the dependent variable in this model. Since the individual will be visiting a doctor in case of an ailment hence the poor the health of the person, the more visits he will be paying to hospitals and the better the person feels, he will be visiting the hospitals less. This indicates that the independent and dependent variables are negatively correlated. The health of an individual might fluctuate due to various reasons. Examples include like that of an epidemic. If a person gets infected in any epidemic then the dependent variable rises. Other examples include being involved in an accident or fire. Such variations in health, the independent variable will cause a surge in the visits to hospital thereby affecting (increasing) the dependent variable.

Hence the model of regression obtained by considering the health of an individual as the independent variable and the number of visits he/she pays to the hospital as the dependent variable serves as an example of real life problem in regression which is negatively correlated.

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