What is Regression? The Minitab handbook says that "Regression allows you to investigate and model the relationship between a response (dependent) variable and one or more predictors (independent variables). Regression can also be used to 'predict' or estimate a future response based on the values of the predictor variables.
In a simple regression, there is one dependent variable and one response variable. The model can be represented graphically as a straight line. Let us see how we can set up a simple regression using the case we have been working on with the two sets of marks. You will see that you will arive at the same conclusion we had previously arrived at, only using a different path. First of all, we have to decide on which will be the response variable. Let us take the English marks as the response and then of course, the Mathematics marks will become the independent set.
Insert the two data sets into a Microsoft Excel spreadsheet as before. This time in the Tools > Data Analysis, select "Regression". You want the simple linear regression. The model can be represented as: y = mx + c, where y is the English mark, and x is the Mathematics mark. Microsoft Excel can give you your results again. you just need to be able to make sense of the numbers, and interprete the results. Look at the results of the analysis. The mass of numbers looks forbidding, but we shall untangle the mess.
What you are looking for is the dependance of the dependent variable on the independent variable. Look at the probability ass ociated with the independent variable. The probability is rather high. recall that in probability terms, a value near 1.000, such as 0.8956 means that there is a good probability that the event will take place. A probability of 0.0002 means that there is a small probability that the event will take place.
It is evident here that there is a significant probability that the English marks are dependent on the Mathematics marks. That is we have no evidence to discount the Null Hypothesis and we conclude that there is liklihood of a relationship between these marks. The simple linear regression gives you a model for the relationship as well.
We have now examined the main analytical aspects of any research project. I shall now turn to the actual administrative process of creating a project proposal and marching through the stages for preparation of the research and finally making your submission for defense.