Question

Regression analysis is often used to provide a means to express the relationship between one or more input variables and a result. It is easy to plot in Excel (“add trendline”) so is found frequently in business presentations. Your company has made a model with 10 different factors measured from past years’ and states based upon the model, the company expects to make a 23 million dollar profit next year. Discuss possible concerns with banking on the 23 million dollar prediction, including concepts of

a. correlation

b. causation

c. single point prediction (that is, just plugging the values into the equation and saying that single number is the prediction of future performance)

d. confidence interval.  

e. prediction interval.

Answer 1

a) Correlation: The correlation gives evidence that how the data values are correlated based on the observed data. Here the correlation between the variables is used to predict the data point of the future event. Hence the prediction of the future data point is the result of correlation.

b) Causation: The causal relationship between two variables occur if one variable really affects the other. This is also called the cause and effect relationship where we manipulate one variable and measure the variation in the other variable. In the regression analysis, the study is based on the past years' observed data hence the prediction of the future data point is not the result of causation.

c) Single point prediction: The prediction of 23 million dollar profit is a result of single-point prediction where we use the data fit model (regression model) and compute the single point based on different independent variables used in the model.

d) Confidence interval: The confidence interval gives the range of data values of mean response (dependent variable) for the input setting (independent variable). Since 23 million dollars profit is a point estimate we are not concerned with a confidence interval.

e) Prediction interval: The prediction interval gives the interval where the next predicted data value would be. Since 23 million dollars profit is a point estimate we are not concerned with the prediction interval