© Buddy Freeman, 2015

1. Independence of error assumption. In many business applications usingregression, the independent variable is TIME. When the data (Yi) is collected at regular

intervals of time you have a time series.

In such cases the errors are likely not to be independent of one another. That is, the error in time frame t is probably correlated with the error in time frame (t+1). If this situation exists, it violates the independence of error assumption, and any results derived from the regression model (however perfect the "fit" may be) are questionable.

ii YY ˆ

© Buddy Freeman, 2015

Each Excel workbook in

S:\BFREEMAN\QM3620\Course Files\Segment3\ExcelFiles\Simple Linear Regression and Correlation

contains a worksheet labeled “Independence of Error”that provides the calculation of the Durbin-Watson statisticto test for such violations. However, the test is not always yes or no. It has a “we are not sure” portion. You need a table of "ranges" to determine if:  (a) The assumption is valid for our model and . (b) The assumption is not valid for our model and . (c) We are not sure if the assumption is valid or not for our model and .

© Buddy Freeman, 2015

2. Equality of Variances assumption. This assumption can be tested by examining a plot with the predicted values on the horizontal (X axis) and the “standardized errors” (Studentized residuals) on the vertical (Y axis). Each Excel workbook in

S:\BFREEMAN\QM3620\Course Files\Segment3\ExcelFiles\Simple Linear Regression and Correlation

contains a worksheet labeled “Equal Variances”that provides the values of the Studentized residuals and thepredicted values used to generate a graph to test for such violations. To make the graph display the data properly, one has to set the X Values to the range of Predicted Y values in column B.

© Buddy Freeman, 2015

If this assumption is violated you will probably see "triangular" patterns. If the pattern has a fairly constant "height" across the range of the predicted values, the assumption isprobably valid. Even if it is violated, sometimes you can still come up with a valid model by applying a "correcting" transformation.

© Buddy Freeman, 2015

3. Normality assumption. 

You can use the Histogram tool in Excel’s Data Analysis Tools to build a histogram of the errors and see if they appear to be normally distributed.

As long as it is not "too" nonnormal, you will have a valid model. Regression is "robust" with respect to the normality assumption.

For a more rigorous normality test, you may use the usethe Anderson-Darling goodness-of-fit test for normality.

© Buddy Freeman, 2015

Each Excel workbook in

S:\BFREEMAN\QM3620\Course Files\Segment3\ExcelFiles\Simple Linear Regression and Correlation

contains a worksheet labeled “Normality” that provides the values of the errors (Residuals). Use the cursor to select all the Residuals.Copy them and perform a paste special (Values) under the heading“Sorted Residuals.” Click on the symbol at the top to

sort these values into ascending order. The approximate P-Valuemay then be used to assess the assumption of normality.

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