# Compression Analysis Of Linear Regression And Correlation

2250 Words 9 Pages
Register to read the introduction…  The relationship between the variables is linear.  Both variables must be at least interval scale.  The least squares criterion is used to determine the equation.

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Regression Analysis – Least Squares Principle

The least squares principle is used to obtain a and b.  The equations to determine a and b are:

n( XY )  ( X )( Y ) b n(  X 2 )  (  X ) 2 Y X a b n n

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Illustration of the Least Squares Regression Principle

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Regression Equation - Example
Recall the example involving Copier Sales of America. The sales manager gathered information on the number of sales calls made and the number of copiers sold for a random sample of 10 sales representatives. Use the least squares method to determine a linear equation to express the relationship between the two variables. What is the expected number of copiers sold by a representative who made 20 calls?

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Finding the Regression Equation - Example

The regression equation is : Y  a  bX Y  18.9476  1.1842 X Y  18.9476  1.1842(20) Y 
The means of these normal distributions of Y values all lie on the straight line of regression.  The standard deviations of these normal distributions are equal.  The Y values are statistically independent. This means that in the selection of a sample, the Y values chosen for a particular X value do not depend on the Y values for any other X values.

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Confidence Interval and Prediction Interval Estimates of Y
•A confidence interval reports the mean value of Y for a given X. •A prediction interval reports the range of values of Y for a particular value of X.

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Confidence Interval Estimate - Example
We return to the Copier Sales of America illustration. Determine a 95 percent confidence interval for all sales representatives who make 25 calls.

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Confidence Interval Estimate - Example

Step 1 – Compute the point estimate of Y In other words, determine the number of copiers we expect a sales representative to sell if he or she makes 25 calls.

The regression equation is : Y  18.9476  1.1842 X Y  18.9476  1.1842(25)
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^ ^

Y  48.5526

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