Problem 1:

Provide me a 1.5 pages of discussion and answer each question in detail. Also Label each question with each question's answers. Make sure you pay close attention to detail on this discussion.

Developing a multiple regression model requires judgment, skill and often times several iterative steps. Even though automatic model building procedures (e.g., stepwise, best subsets) are helpful, we still need to evaluate the adequacy and suitability of the resulting multiple regression model in practice. What are some of the issues relevant to forecasting with multiple regression models? Just because a multiple regression model is statistically significant, does that mean it will do a good job forecasting? Because we are now dealing with a statistical model, we have the ability to develop different types of forecasts. What is the difference between a point forecast, a confidence interval forecast, and a prediction interval forecast? Can you give an example of each within the context of a specific scenario with which you are familiar? Which of the three do you think is most applicable in business forecasting?

Problem 2:

Provide me a half page response to each of the following two discussion posts. Tell me what you agree with and/or disagree with and if there is anything that you disagree with then provide any alternatives. Once again, pay close attention to detail in each of the following two discussions and label each discussion with the response to each.

Discussion 1:

When developing a multiple regression model choosing suitable predictor variables is important because if they are too closely correlated then the forecast will not be improved. One needs to figure out how many predictor values to use that might add accuracy to the forecast, however cost needs to be taken into consideration at the same time. This is where judgment comes in because finding a suitable number of predictors for your equation while keeping it simple and cost effective is the goal. So when building a multiple regression model you need to be able to use your judgment in the selection process.

Some of the issues that may be encountered are measuring the strength between the independent variables and the dependent variable. This analysis can lead to wasted computer time and physical time deciphering the outcomes. Also, if there are a lot of variables for the system to analyze it might choose to use some that are insignificant to the accuracy of the forecast. If the independent variables are too correlated then multicollinearity can occur which may cause computational difficulties and large stand errors. Overall it is a complex process from start to finish.

Based on previous experience multiple regression could be used by a car company to predict how well a particular new model will sell. Independent variables could be family size, age, income, gender, or geographic location. Dummy variable should also be introduced to the equation to determine if there are relationships between independent variables and the dependent variable. If there is multicollinearity present then it needs to be determined which independent variable should be dropped and judgment would come into play. The goal is to create a way to understand the present in hopes to better predict the future.

Discussion 2:

When using a multiple regression model, the first decision (besides what you would like to predict) is the selection of independent variables, or predictor variables. The best outcome is basically to achieve the highest R-squared value possible, but to do so with the least number of variables possible, specifically those variables that significantly contribute to an R-square increase. A large degree of judgement and experience on the forecaster's part is important here. Predictor variables should not be significantly correlated with each other (multicollinearity). Deletion of seemingly insignificant variables is an exercise of trial-and-error (t-tests). Removal of one variable affects the remaining ones and changes their statistical significance (t-values, or P-values in Minitab).

For example, if I wanted to predict the amount of commercial small business loan defaults for next quarter, I could use possible determinants: delinquency rates, debt service coverage ratios, unemployment rates, credit scores of principals, debt-to-income ratios of principals, instances of past-due property taxes. It is possible that two variables like the owners' credit scores and debt-to-income ratios may be intercorrelated and we would need to use only one to avoid multicollinearity which creates unstable forecast values. Delinquency rates may present some of the typical problems posed with time-series data in regression analysis. While this data is not usually affected by the season or time of year, it does exhibit behavior similar to seasonality because in the "short" months of February, April, June, September, and November there is a decline in number of delinquencies that hit the 30-day, 60-day, or 90-day status. This data would probably need to be adjusted before it was fit to use for regression. Again, it would take a good degree of judgement by the forecaster to determine which of the independent variables were actually helpful in producing a good forecast and which ones were not significant, and should be removed.