Prior to beginning work on this discussion forum, read Chapter 11: Regression Analysis: Statistical Inference, paying attention to Section 11-7 on outliers and Figures 11.13, 11.14, and 11.15. Additionally, read Chapter 12: Time Series Analysis and Forecasting.

For this discussion,

Assess the use of various decision support 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.

As you might imagine, regression analysis can be used for a wide range of applications. For example, suppose that you want to predict the number of visitors from one week to the next based on the number of visitors during each week. This is an example where linear regression could be used. In this case, we have two independent variables (i.e., weeks) and one dependent variable (i.e., number of visitors each week).

Regression analysis is a statistical method used to predict the value of one or more of the dependent variables based on the values of one or more independent variables. The regression equation is used to predict the value of the dependent variable, and then this relationship can be graphed.

The regression analysis will use different forms depending on how many independent variables you have and whether they are continuous or categorical (categorical being any factor that can be described by a discrete number).

Commonly known as linear regression, regression analysis is used to identify relationships between variables, predicting the value of a dependent variable as a result of values of an independent variable. For example:

- If you have data on how much people weigh and whether they are male or female, then you could use linear regression to predict how much weight each person would be expected to weigh given their gender. In this case, the slope coefficient (gradient) tells us how much weight will change for each ten-unit increase in gender; therefore, we can say that there is an inverse relationship between gender and weight gain/loss.
- Another example might be if you had data related only to height differences between boys and girls but no information about race or ethnicity—then your task would be finding out if there was any correlation between height differences among different races or ethnicities!

The goal of regression analysis is to find the best possible relationship between an independent variable and a dependent variable (y). In other words, it aims to estimate how much change in y can be predicted by changes in x.

In this chapter you’ll learn about:

- Basic notation for regression analysis
- The basic steps involved in performing a linear regression
- When should you use multiple regressions?

Consider two related examples where each has a single dependent variable (y) and two independent variables (x1 and x2). The resulting equation for this example is y = ax1 + bx2. This simple equation shows that if we change x1 we should also expect some change in y- that is, we expect to see some changes in our dependent variable under specific circumstances.

In the first example, if you add one more digit to your phone number, your new phone will be able to receive calls from any area code as long as it’s dialed correctly by using touch-tone keys on each end of the line (or even just manually entering numbers into phones with rotary dials). In other words: Adding another digit will allow us to travel around more easily! However…

In the previous examples, we showed how regression analysis can be used to predict changes in dependent variables as a result of changes in independent variables. The goal of regression analysis is to find the best possible relationship between an independent variable and a dependent variable (y). In other words, it aims

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