Vol. 8, No. 7

July 2006

PQ Systems

SQCpack real-time charting

Quality Quiz: With a video!

Six Sigma

Data in everyday life

Bytes and pieces

FYI: Current releases


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Quality Quiz from Professor Cleary

"No" is correct.

Click here for a more complete video explanation

No, although there's nothing wrong with looking at this data by means of run charts. In fact, depending on what he's trying to analyze, it may be the perfect tool for this data.

But a second option would be to examine the relationship between cost and output, rather than separately examining each factor in a run chart. A scatter diagram helps to look at the relationship of the two.

The regression line in simple linear regression is a straight line drawn through the points plotted on the scatter diagram. The calculation results in an equation where the value of Y (on the vertical axis) can be predicted from the value of X (on the horizontal axis a). The equation takes the form of:

The equation is then used to draw a straight line through the points. The aim is to achieve a line of best fit, where the difference between the actual points plotted and the line is minimized. This concept is shown graphically below.

To determine this line requires an estimate of the regression coefficients a and b. The formulas to determine these coefficients are shown below:

The value of b must be calculated before a. To find b, a number of calculations are required. To simplify this process, a table is constructed, showing the values of X and Y, and the calculated values of XY, Y2, and X2. The table for the example follows:

Therefore, the average value of X and Y are:

The value of b can be found by using the values calculated in the table. In the equations below,"n" represents the number of pairs of data used in the analysis. In the example, n is 10.

The value of a can then be calculated as follows:

Therefore, the regression line has an equation of:

Of course, it isn't necessary to do all these calculations by hand. Just use CHARTrunner to derive the regression line without having to use a single formula. Next month: Kohl Minor faces t-tests.

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