Single Regressor or Simple Regression Model:

Single Regressor or variable (x) that has a relationship with response (y).  Creates a straight line.

What to look for, example from our book: 

Bruce L. Bowerman, and Richard T. O'Connell, From Miami University, Business Statistics in Practice, 3rd, McGraw-Hill Irwin, Page 547, Example 11:1 and Figure 11.1.

 

Regression Lines

 

by Venita Twitty, (UoPhx 2008) 

 

The regression lines are used for a visual method of relating the relationship between (x) and (y) in a graph. The (x) is independent variable and (y) is a dependent variable. Independent refers to the process of one event has no impact on another event. Dependent is if the process has an impact on an event. The equation for the line used to estimate Y based on X referrers to as the regression equation (Lind, Marchal & Wathen, 2005, p. 440).

 

The Regression Equation is a line in a two-dimensional or two-variable space is defined by the equation Y=a+b*X; in full text: the Y variable can be expressed in terms of a constant (a) and a slope (b) times the X variable. The constant is also referred to as the intercept, and the slope as the regression coefficient or B coefficient (Linear Regression in Excel, 2004).

 

            An example of solving and defining regression is outlined in the following example. The example is found at North Carolina University Labwrite website.

 

A method for making predictions given 2 related variables (related means variables which are correlated). The form of the prediction is usually: what is the expected y value given some x value.  The form of the regression line is: Predicted y = (slope) multiplied by (X value) + intercept.

 

     Steps to compute regression line:

  • Find slope (correlation multiplied by the standard deviation of y) *divided by*       (standard deviation of x)

  • Find intercept (mean of y minus* (slope multiplied by mean of x))

  • Plug in x and solve for y

 

  Note, predictions are only good when:

  • The x values you want to use come from the same population that the regression equation was derived from and

  • The x values you want to use are within the range of the original x variable

 

 

 

 

References

 

Lind, Marchal & Wathen. (2005). Statistical Techniques in Business & Economics, 12 ed. [University of Phoenix Custom Edition e-text]. New York: The McGraw-Hill Companies. Retrieved July 10, 2008, from University of Phoenix, rEsource,

 

MBA/510- Statistical Techniques in Business & Economics Web site.

North Carolina University. (2004). Linear Regression in Excel.  Retrieved August 18, 2008 from: http://www.ncsu.edu/labwrite/res/gt/gt-reg-home.html

 

 

Multiple Regressors or Multiple Regression Model:

More than one Regressor or variable (Xi) that has a relationship with response (y).  Creates a straight plane.

What to look for, example from our book: 

Bruce L. Bowerman, and Richard T. O'Connell, From Miami University, Business Statistics in Practice, 3rd, McGraw-Hill Irwin, Page 526 and 527, Example 12:1, Table 12.1 and Figure 12.3.

 

Curvilinear or Polynomial Regression Model or Quadratic Regression Model:

Curve or variable (X squared) that has a relationship with response (y).  Creates a curved line.

What to look for, example from our book: 

Bruce L. Bowerman, and Richard T. O'Connell, From Miami University, Business Statistics in Practice, 3rd, McGraw-Hill Irwin, Page 552 and 553, Example 12:11, Table 12.8 and Figure 12.14.