Regression analysis can be used to analyze how a change in one variable impacts the other variable, such as an increase in a marketing budget increasing sales. Find a unique area of your life where one variable impacts the other variable (being sure that are both measurable) and do a regression analysis on it. Remember to include the coefficient of determination as well as the test of significance. Share your results and make any comments as to whether or not there is a possibility of potential problems (causation or extrapolation) with your results.
Here can be a real life scenario, the city council of of a city can consider increasing the number of police in an effort to reduce crime! Being from Chicago this is becoming more and more relevant in our city. Every year it seems they add another thousand officers or so.
For this lets take some supporting data for the past few months on the police employed and crimes that took place, both of which are measurable
Crime: 20, 16, 9, 11, 9, 21, 24, 10
Police: 25, 26, 32, 35, 26, 21, 20, 28
The number of crimes depends on the police employed. So, dependent variable (Y) = Crime and independent variable (X) = Police. The regression output is as follows-
Regression Equation is: Y=40.3113-0.9506X
When the number of police officers is 0, then as per the model, the average crime rate=40
The number of Crimes is negatively correlated with the Police employed and the correlation factor is -0.9506
R-Square/ Coeffifcient of Determination is 0.63
It means that the model explains 63% relationship between the variables taken for consideration
The t-stat are the significant tests employed here.