Outliers Due In 11 Hours For This Discussion

Outliers Due In 11 Hoursfor This Discussion You Will Asse

DQ #1: Outliers (Due in 11 hours)!!! For this discussion, you will assess the use of various support decision tools and explain why outliers are sometimes called influential observations. Discuss what could happen to the slope of a regression of Y versus a single X when an outlier is included versus when it is not included. Will this necessarily happen when a point is an outlier? You are required to give at least two examples in your response.

DQ #2: Correlations/Linear & Multiple Regression (Due in 48 hours)!!! Note that this discussion is due on Day 6. Although the initial post is due on Day 6, you are encouraged to start working on it early as it includes work in Excel. Prior to beginning work on this assignment, read Chapter 10. Complete Problem 50 in Chapter 10 on page 477. 10-55) A golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales. Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = ab^X), and multiplicative (Y = aX^b). Which equation fits the data best? Interpret your best-fitting equation. Using the best-fitting equation, predict sales during a month in which the price is $470. In the discussion area, attach the Excel document showing work.

Paper For Above instruction

Outliers are data points that deviate markedly from the overall pattern of data. They are sometimes called influential observations because they can disproportionately affect the outcome of statistical analyses, especially regression models. Understanding how outliers influence models is critical in data analysis, as they can lead to misleading results if not identified and appropriately handled.

Support decision tools such as regression analysis, correlation coefficients, and other statistical models are essential in analyzing data and making informed decisions. However, the presence of outliers can significantly impact these tools. Outliers can skew the estimated parameters, distort measures of association, and lead to incorrect conclusions about the relationships among variables. This is especially true in simple linear regression, where an outlier can substantially alter the estimated slope and intercept, influencing the interpretation of the relationship between the independent and dependent variables.

Outliers are called influential because they can exert a disproportionate effect on the fitted regression line. For instance, consider a dataset where the true relationship between X and Y is linear with a slope of 2. If an outlier with a very high X value and a corresponding Y value that is not consistent with the overall pattern is included, it can inflate or deflate the estimated slope. Conversely, when the outlier is removed, the slope may revert closer to its true value, highlighting its influential nature.

To illustrate, suppose in analyzing the relationship between advertising expenditure and sales, a data point at an unusually high advertising spend with very low sales could skew the regression line downward, suggesting a negative relationship, which is counterintuitive. Removing or adjusting for this outlier would likely show a positive relationship consistent with the majority of data points.

Similarly, in the context of medical research, an outlier patient with an extremely high response to a drug could influence the estimated effectiveness of the treatment if included in the analysis, potentially leading to overestimation. Removing this influential point might provide a more accurate estimate of the drug's typical effect.

Regarding the impact on the slope of a regression model when an outlier is included, it is not necessarily always the case that the slope will change significantly. Some outliers may not influence the regression line if they lie close to the existing pattern, but high-leverage points—those with extreme predictor values—are more likely to alter the slope noticeably.

Understanding the distinction between outliers and leverage points is essential. Outliers are identified based on their response (Y), while leverage points are identified based on their predictor variables (X). High-leverage points can influence the slope even if they are not traditional outliers in terms of Y.

In conclusion, outliers and influential observations can significantly impact regression outcomes and decision-making tools. Recognizing these points through residual analysis, leverage statistics, and influence measures such as Cook's distance is vital. Removing or appropriately addressing influential observations ensures robust and reliable models, leading to better data-driven decisions.

References

• Chatterjee, S., & Hadi, A. S. (2015). Regression Analysis by Example (5th ed.). Wiley.
• Cook, R. D., & Weisberg, S. (1982). Residuals and Influence in Regression. Chapman & Hall.
• Hamilton, L. C. (2009). Statistics with Stata: Version 11. Cengage Learning.
• Kleiber, C., & Zeileis, A. (2008). Elements of Statistical Computing in R. Springer.
• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis. Wiley.
• Rousseeuw, P. J., & Leroy, A. M. (2005). Robust Regression and Outlier Detection. Wiley.
• Salkind, N. J. (2010). Statistics for People Who (Think They) Hate Statistics. Sage Publications.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Pearson.
• Weisberg, S. (2005). Applied Regression Analysis (3rd ed.). Wiley.
• Yilmaz, M. (2015). Detecting Influential Data Points in Regression Analysis. Journal of Applied Statistics, 42(3), 585-599.