What does the intercept of a regression tell? What does the slope of a regression tell?

Part 1

Bivariate Regression

Regression analysis is a powerful and commonly used tool in business research. One important step in regression is to determine the dependent and independent variable(s).

In a bivariate regression, which variable is the dependent variable and which one is the independent variable?

• What does the intercept of a regression tell? What does the slope of a regression tell?
• What are some of the main uses of a regression?

Provide an example of a situation wherein a bivariate regression would be a good choice for analyzing data.

Justify your answers using examples and reasoning. Comment on the postings of at least two peers and state whether you agree or disagree with their views.

Types of Regression Analyses

There are two major types of regression analysis—simple and multiple regression analysis. Both types consist of dependent and independent variables. Simple linear regression has two variables—dependent and independent. Multiple regression consists of dependent variable and two or more independent variables.

• How does a multiple regression compare with a simple linear regression?
• What are the various ways to determine what variables should be included in a multiple regression equation?
• Compare and contrast the following processes: forward selection, backward elimination, and stepwise selection.

Part 2

Multiple regression analysis is widely used in business research in order to forecast and predict purposes. It is also used to determine what independent variables have an influence on dependent variables, such as sales.

Sales can be attributed to quality, customer service, and location. In multiple regression analysis, we can determine which independent variable contributes the most to sales; it could be quality or customer service or location.

Now, consider the following scenario. You have been assigned the task of creating a multiple regression equation of at least three variables that explains Microsoft’s annual sales.

Use a time series of data of at least 10 years. You can search for this data using the Internet.

• Before running the regression analysis , predict what sign each variable will be and explain why you made that prediction.
• Run three simple linear regressions by considering one independent variable at a time
• After running each of the three linear regressions, interpret the regression.
• Does the regression fit the data well?
• Run a multiple regression using all three independent variables.
• Interpret the multiple regression. Does the regression fit the data well?
• Does each predictor play a significant role in explaining the significance of the regression?
• Are some predictors not useful?
• If so, did you consider removing those and rerunning the regression?
• Are the predictors related too significantly to one another? What is the coefficient of correlation “r”? Do you think this “r” value suggests a strong correlation among the predictors ( the independent variables?