DISCUSSION 1
Based on the text on regression assumptions and your additional research, discuss the potential impact of assumption violation on interpretation of regression results.
As a business owner, it is important to be able to accurately predict which direction your business is heading. There are many variables that may be used to achieve that such as the number of customers per month versus sales for that month spread out over a particular time period. Whatever the variables are, the relationship between these variables is what is truly important to establish so that predictions can then be made. Regression analysis is one of the most important techniques used to help estimate the strength and direction of the relationship between the variables used. In other words, an analyst can use the results of regression analysis to show whether the relationship is valid (Anderson, n.d.); whether there is any violation of the assumptions used to build the relationship. Just a few of those assumptions are 1) Normal distribution of residuals, 2) Homoscedasticity, and 3) Linearity. Moderate violations of these assumptions do not pose a serious problem for testing the significance of predictor variables, however small violations can pose problems for confidence intervals on predictions for specific observations (Trident Learning Community, n.d.). In other words, small violations of the above-mentioned assumptions can cause predictions on a specific point in the future to stray from actual values outside of the confidence interval boundary. Therefore, if you, as the business owner, are making significant business decisions based on these variables that have violated the assumptions, you could be steering your business in a direction that may not return the results that have been forecast or may not return the results you are hoping to attain by making a decision based on a faulty forecast.
Reference
Anderson, A. (n.d.). Business Statistics: Use Regression Analysis to Determine Validity of Relationship. Retrieved on July 30, 2018, from https://www.dummies.com/education/math/business-statistics/business-statistics-use-regression-analysis-to-determine-validity-of-relationships/
RESPONSE 1
The assumptions for the regression test, which reveals the strength, direction, and authenticity of relationship, are few; however, these assumptions must be observed to obtain valid results. For instance, it is imperative to not to gather such data, pertaining to selected variables, which is similar. This similarity in data, related to different variables, impairs the quality of overall data and that results that are produced by applying statistical tests are not valid or authentic.
You are right that when violation of these assumptions is serious, the results obtained are highly flawed or invalid. Relying on such results for decision making would have serious consequences, especially in the long run. I disagree with this assertion that moderate violation of assumptions may not have serious consequences. I believe that moderate violations may not have serious consequences in the short-term, but in the long-term, minor and moderate violations would have serious consequences.
Question
Can we rely entirely on post-analysis tests to determine the validity of tests?
DISCUSSION 2
Is there any influence of the assumption violation on the business decision making? If so, how? If not, why?
In the personal research done I discovered that it was best to understand what a regression analysis was. I was able to find that regression analysis is a very useful instrument when attempting to predict an outcome. In the business world, this statistical process can be used to forecast consumer trends, profits and future costs. Using a straight line in the graph and being able to identify the y-intercept of the line and the slope will allow foretelling the average of y from x (Using Linear Regression to Predict an Outcome, n.d) When interpreting the outcome of a linear regression, assumption violation may have a great impact when analyzing the data. For example, a medical insurance company might want to issue a new insurance premium cost and use a linear regression to predict the suggested cost for it, but the violation of assumption can bring some faulty results. When making business decisions violation of the following will bring inaccurate products, heteroscedasticity, multicollinearity, and autocorrelation. An assumption has a lead role in the business world since they determine the overall business opportunities and financial health.
Reference
Using Linear Regression to Predict an Outcome. (n.d.). Retrieved from https://www.dummies.com/education/math/statistics/using-linear-regression-to-predict-an-outcome/
RESPONSE 2
There is no denying the fact that regression and correlation tests have great relevance and application in the corporate world. In fact, large corporations rely on these tests to understand the impact (strength and nature of direction) of independent variables on dependent variable (s). However, it is essential to observe basic assumptions of regression tests in order to obtain valid or reliable tests. The reliability of results is the basis of a good decision, which is why the entire emphasis is on obtaining authentic and valid results.
You have rightly pointed out that the consequences of violating basic assumptions of regression are dire and when the data is enormous, even minor violations can pollute the results and make them faulty and unreliable. Therefore, when applying for a regression test, one must consider these assumptions very diligently. For that one must have comprehensive understanding of 1) normal distribution, 2) Homoscedasticity, 3) Hetroscedasticity, 4) Multicollinearity and 5) Linearity.
Question
How accurately do post-analysis tests reveal validity of tests?
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