Outliers

Assess the use of various support decision tools.

Below are some of the support decision tools;

Paradigm models- These models help in handling situations. They include, perspectives, paradigms and the frameworks.

Representation aids- They are techniques that assist in visualizing data. They may include diagrams, projectors, and charts among others.

Information control- Important for organizing, storage, gathering and retrieval of data.

Simulation models- They are important decision making tools that helps in answering the ‘what if’ questions.

Ways of choosing- They are the various tools and techniques that help to narrow down choices.

Explain why outliers are sometimes called influential observations.

Outlier refers to those points that falls away from the rest of the points in a scattered plot. In other words, they do not follow the trend of the data set. They may be termed as data containing errors or indicates a regression line that fits poorly.

Outliers can be termed as influential observation when such points falls further from the rest of the data in a horizontal direction(“Linear Regression”). The distinction follows the fact that the points have huge impact on the Y intercept and the slope. The term influential observation can also be used when outliers have much bigger residual or appears like a horizontal gap with no points in between.

Discuss what would happen to the slope of a regression of Y versus a single X when an outlier is included versus when it is not included.

The best way to determine the influence of outliers is to calculate the regression with outliers and without. Sometimes influential points is due to bad data, it is there for to check the variation of regression statistics with and without outliers.

When an outlier or outliers are included, the slope will shift in favor of the outlier. The influence point affect the coefficient of determination making it bigger or smaller (“Influential Points in Regression”).

Below is an example of regression line with or without an outlier.

Diagram1

a) has no outliers while diagram b) contains an outlier.

a) b).

Regression equation y= 104.78-4.10x Regression Equation y =97.51-3.32x

Coefficient of determination R^2 =0.94 Coefficient of determination R^2=0.55

The slope containing an outlier tend to be flatter.

Will this necessarily happen when a point is an outlier? Give at least two examples in your response

Sometimes an outlier may result to a line of best fit. This happens when the y intercept tend to remain in its original position. Outliers can results to either smaller or bigger coefficient of determination. In the above case (diagram 1), the coefficient of determination with an outlier is smaller. Below is an example of a larger coefficient of determination.

a). Without an outlier b). With an outlier

Regression equation y= 92.54-2.5x Regression equation y=87.59-1.6x

Coefficient of determination R^2= 0.46 C.o.D R^2 = 0.52