Multivariate Regression Model Analysis Report
The Model Analysis Report provides a summary of the regression analysis that was conducted for the specified multivariate regression model.
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The below table presents a sample Model Analysis Report for Multivariate Regression Forecasting.
Model Analysis Report
MICSCapacity Planner ANALYSIS OF MULTIVARIATE REGRESSION MODELS MODEL OF: TOTCPUTM BASED ON: TSOCPUTM IMSCPUTM CICCPUTM --------INDEPENDENT--ELEMENTS-------- R**2 F P INTERCEPT NAME COEFFICIENT F P -------- ------- ----- --------- -------- ----------- ------- ----- 0.97 1127.97 .0001 10:57:58.3 TSOCPUTM 1.77499 71.77 .0001 IMSCPUTM 1.14392 77.90 .0001 CICCPUTM 1.13065 31.88 .0001
The Model Analysis Report contains the following information:
MODEL OF
The dependent data element that you want to forecast.
BASED ON
The independent data elements on which the analysis is based.
The first four columns of the report are discussed below.
R**2
The r-squared value for the model. Although the SAS REG procedure attempts to use every one of the independent elements suggested by the analyst, the procedure excludes any term that does not result in a minimum improvement in the r-squared value as specified on the Multivariate Regression Forecasting screen. We recommend an r-squared value of 0.70 and above for the acceptance of models produced with Multivariate Modeling Forecasting.
F
The F statistic for the model. As discussed in Evaluating the Multivariate Regression Model, the F statistic is calculated from the ratio of sums of squares of the model. Larger F values indicate a more reliable model. The F statistics might be unreliable for models developed with a small number of points (that is, less than 30). An F value is provided for each step made by the regression procedure.
P
The probability that the model proposed is significant (that is, more reliable than forecasting the average value of the historical observations). Although most statistics texts recommend testing the null hypothesis to a 0.001 level, we recommend 0.01 for models based on computer measurement data. A p value is provided for each step made by the regression procedure.
INTERCEPT
The b value for the regression equation.
The next four columns are produced for each independent element that you specify. These columns contain the following information:
NAME
The name of the independent element being analyzed.
COEFF
The coefficient for the independent element in the regression equation. Negative coefficients indicate that you can expect resource consumption to decrease with increases in the independent element value. This situation is usually not normal in resource consumption models.
F
The F statistics calculated for the business element. This F value indicates the significance of the independent element in the model that was developed. Once again, larger values indicate a more reliable model and the value might be misleading for models based on small samples.
P
The probability that the specified business element makes a significant contribution to the model developed. We recommend a 0.01 acceptance value.
This report is used to evaluate whether the model that is produced adequately models an application. Although the values of r-squared, F, and p indicate the statistical significance of the proposed model, remember that a proper evaluation includes all three tests enumerated in Evaluating the Multivariate Regression Model: statistical interpretation, visual inspection, and the common sense test.