Linear Regression Analysis
Mary Ann Fiene, MT(ASCP), Alan K. Reichert, PhD.
The purpose of this course is to demonstrate how to use linear regression to predict the value of one variable, given the value of the other variable and the experimental data concerning the relationship between the variables.
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Continuing Education Credits
Objectives
- Define linear regression and explain how it is used.
- Given data points which fall on a straight line, find the equation for the line.
- Use the regression equation to predict the value of a dependent variable give the value of the independent variable.
- Explain what is meant by the phrase "line of best fit."
- Given a set of data, determine the best fit using the least squares method.
- Define and calculate standard error of estimate.
- Explain the difference between a, alpha, b, and beta, as applied to regression analysis, and describe why confidence intervals are calculated for the slope and y-intercept.
Course Outline
Click on a link in the outline to view a sample page from this course.
- Introduction to Regression Analysis
- Introduction to Least Squares Method of Best Fit
- Introduction to Least Squares Method
- The Least Squares Line
- Standard Error of Estimate
- Calculate the sum of squares for line B. To do this, you must calculate , the difference y-, and the squared difference (y-img style="vertical-align: ...
- Using the sum of squares from the previous question, calculate the Standard Error of Estimate for line B (to the nearest thousandth).
- Least Squares Calculation
- Determining the Least Squares Line
- Formulae for Determining the Slope and Intercept
- Calculating the Standard Error of Estimate
- Correlation Coefficient
- Example Regression Line Calculation
- Using the Least Squares Formulae
- Determining Se and r2
- Data for Questions
- Using the previous data, calculate the total of the (x-)(y-) values. What is the total?
- Using the same data, calculate the total of the (x-)2 values. What is the total?
- What are the slope and y-intercept of the least squares regression line for this data?
- What is the Standard Error of Estimate for this regression line? You may either calculate for each point, or calculate the sum of y2 and x*y va...
- Calculation of Confidence Intervals for Least Squares
- Confidence Intervals for Slope and Intercept Parameters
- Calculating Confidence Intervals
- Formulae for Confidence Intervals
- Calculate the confidence inteval for α. Use the data of the previous section. You have already calculated the slope and intercept of the reg...
- Now calculate the confidence inteval for b. Use the data of the previous section. You have already calculated the slope and intercept of the regressio...
Additional Information
Level of instruction: Intermediate Intended audience: This course is appropriate for laboratory professionals, and for students in clinical laboratory science programs who want a review of the statistics that are analyzed for assessment of quality control. Author Information: Mary Ann Fiene, MT(ASCP), has authored several articles on the subjects of curriculum development, competency evaluation, and job restructuring. Her articles have appeared in the Journal of Allied Health, American Journal of Medical Technology (now published as Clinical Laboratory Science), and Medical Laboratory Observer.
Ms. Fiene was affiliated as an educator with the Kettering Medical Center School of Medical Technology.
Alan Reichert, PhD, is a professor of finance at Cleveland State University in Ohio. About the Course: This course is part of a series of courses adapted for the web by MediaLab Inc. under license from Educational Materials for Health Professionals Inc. Dayton OH, 45420. Copyright EMHP.
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