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.
Continuing Education (CE) Credits
Other Quality Control & Lab Math Courses
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Linear Regression Analysis 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.
Linear Regression Analysis Outline
- Introduction to Regression Analysis
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Predicting a Value
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A Regression Analysis Example
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A Regression Analysis Example (continued)
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Calculating the Y-INTERCEPT
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Prediction Using the Resulting Equation
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Given the following CREATININE standards:
mg/dL
ABSORBANCE
3
0.14
6
0.26
9
0.38
What is the correct form of the regression line?
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Given the data and linear regression line you calculated on the previous question, what is the expected ABSORBANCE of a 10 mg/dL sample?
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True or false: you should make a SCATTERPLOT of your data before you calculate the regression line.
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Given the following data, calculate the regression line:
x
y
2
9.2
4
8.4
6
7.6
8
6.8
10
6.0
- Introduction to Least Squares Method of Best Fit
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Introduction to Least Squares Method
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The Least Squares Line
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Standard Error of Estimate
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Calculate the sum of squares for line B. To do this, you must calculate , the difference y-, and the squared difference (y-)2 for each point, and then sum the squared differences. You may find it useful to make a chart similar to this one. Some of the data has been filled in for you: The equation for line B is y = x. Use this to calculate the . Pointxyy-(y-)2 1105.010-5.025.0 21824.0 33827.5 45060.0 56350.0 What is the sum of squares (the final column)?
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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
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Determining the Least Squares Line
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FORMULAE for Determining the Slope and Intercept
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Calculating the Standard Error of Estimate
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Correlation COEFFICIENT
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Example Regression Line CALCULATION
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Using the Least Squares FORMULAE
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Determining Se and r2
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Data for Questions
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Using the previous data, calculate the total of the (x-)(y-) values. What is the total?
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Using the same data, calculate the total of the (x-)2 values. What is the total?
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What are the slope and Y-INTERCEPT of the least squares regression line for this data?
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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 values and use the shortcut form.
- CALCULATION of Confidence Intervals for Least Squares
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Confidence Intervals for Slope and Intercept Parameters
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Calculating Confidence Intervals
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FORMULAE for Confidence Intervals
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Calculate the confidence inteval for α. Use the data of the previous section. You have already calculated the slope and intercept of the regression line, as well as the Standard Error of Estimate. Use t0.05 = 1.96.
The 95% confidence interval is:
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Now calculate the confidence inteval for b. Use the data of the previous section. You have already calculated the slope and intercept of the regression line, as well as the Standard Error of Estimate. Use t0.05 = 1.96. The 95% confidence interval is:
Linear Regression Analysis Keywords Click on a term below to see its use in this Linear Regression Analysis course and other available MediaLab courses.
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