Регрессионный анализ в пакетах STATGRAPHICS и MATHCAD

Галушкин И. В. Е-441

Прикладная статистика.

Лабораторная работа № 9.

Регрессионный анализ в пакетах STATGRAPHICS и MATHCAD.

Вариант № 2:

STATGRAPHICS:

Simple Regression - Prod vs. Temp

Regression Analysis - Linear model: Y = a + b*X

----------------------------------------------------------------------------Dependent variable: Prod

Independent variable: Temp

----------------------------------------------------------------------------Standard          T

Parameter       Estimate         Error       Statistic        P-Value

----------------------------------------------------------------------------Intercept        20,3057       0,805699        25,2025         0,0000

Slope           -1,05721      0,0821538       -12,8686         0,0000

----------------------------------------------------------------------------Analysis of Variance

----------------------------------------------------------------------------Source             Sum of Squares     Df  Mean Square    F-Ratio      P-Value

----------------------------------------------------------------------------Model                     146,663      1      146,663     165,60       0,0000

Residual                  6,19946      7     0,885637

----------------------------------------------------------------------------Total (Corr.)             152,862      8

Correlation Coefficient = -0,979512

R-squared = 95,9444 percent

R-squared (adjusted for d.f.) = 95,365 percent

Standard Error of Est. = 0,941083

Mean absolute error = 0,763126

Durbin-Watson statistic = 2,93311 (P=0,0175)

Lag 1 residual autocorrelation = -0,553525

The StatAdvisor

--------------The output shows the results of fitting a linear model to describe

the relationship between Prod and Temp.  The equation of the fitted

model is

Prod = 20,3057 - 1,05721*Temp

Since the P-value in the ANOVA table is less than 0.01, there is a

statistically significant relationship between Prod and Temp at the

99% confidence level.

The R-Squared statistic indicates that the model as fitted explains

95,9444% of the variability in Prod.  The correlation coefficient

equals -0,979512, indicating a relatively strong relationship between

the variables.  The standard error of the estimate shows the standard

deviation of the residuals to be 0,941083.  This value can be used to

construct prediction limits for new observations by selecting the

Forecasts option from the text menu.

The mean absolute error (MAE) of 0,763126 is the average value of

the residuals.  The Durbin-Watson (DW) statistic tests the residuals

to determine if there is any significant correlation based on the

order in which they occur in your data file.  Since the P-value is

less than 0.05, there is an indication of possible serial correlation.

Plot the residuals versus row order to see if there is any pattern

which can be seen. 

Analysis of Variance with Lack-of-Fit

----------------------------------------------------------------------------Source             Sum of Squares     Df  Mean Square    F-Ratio      P-Value

----------------------------------------------------------------------------Model                     146,663      1      146,663     165,60       0,0000

Residual                  6,19946      7     0,885637

----------------------------------------------------------------------------Lack-of-Fit            6,19946      7     0,885637                       

Pure Error                 0,0      0            

----------------------------------------------------------------------------Total (Corr.)             152,862      8

The StatAdvisor

--------------The lack of fit test is designed to determine whether the selected

model is adequate to describe the observed data, or whether a more

complicated model should be used.  The test is performed by comparing

the variability of the current model residuals to the variability

between observations at replicate values of the independent variable

X.  Unfortunately, the test can not be run in this case because there

are no replicate observations at the same values of Temp. 

Predicted Values