ASP Statistical Software A STATISTICAL PACKAGE (ASP) For Business, Economics, And The Social Sciences

# Regression

## Regression Models

ASP allows you to estimate seven kinds of regression models:

• Simple Regression.
• Multiple Regression.
• Weighted Least Squares.
• N Way Autocorrelation.
• Two Stage Least Squares.
• Stepwise Regression.
• Binary Logit Regression.

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## Basic Regression Output

Regression output is generated and displayed in two stages:

1. First, a table of coefficients and other statistics is generated and displayed.

2. You are then given option for generating additional output from the model being estimated.

• Table Of Coefficients. For most routines the table of coefficients and statistics includes:

• An algebraic representation of the equation being estimated.
• A table that lists the estimates of the coefficients in this equation.
• The values of the t statistics, along with their associated degrees of freedom and probability values, for the null hypotheses that each individual coefficient is zero.
• The partial R square for each of the independent variables.
• The standard errors of the individual coefficients.
• Other Basic Statistics. Other basic statistics of the model being estimated are displayed below the table of coefficients. These include:

• R square.
• Durbin Watson statistic.
• Standard error of estimate.
• F statistic and its degrees of freedom and probability value for the null hypothesis that the coefficients of all variables other than the constant term are zero.

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Once the table of coefficients and other statistics is exited you are given eight options for additional output:

• Plot/List/Add Residuals To Data Matrix. This option allows you to:

• Calculate and plot the standardized, Studentized, and jackknife residuals along with the leverage and influence of each residual.
• Calculate a table of the actual value of the dependent variable, its estimated value, and the residual values.
• Variance/Covariance Matrix. This option allows you to list the variance/covariance matrix for the coefficients of the model being estimated.

• Beta Weights. This option allows you to list the beta weights associated with each independent variable in the model being estimated.

• Forecast Dependent Variable. This option allows you to use the model being estimated to forecast the dependent variable with four kinds of confidence limits:

• Single Period Confidence Limits.
• Scheffe Confidence Limits.
• Bonferroni Confidence Limits.
• Working-Hotelling Confidence Limits.

The output generated by this routine depends on the kind of confidence limits you have chosen, but, in general, includes:

• Forecasted values generated.
• The mean and expected value of the forecasted values.
• The standard errors of the forecasted values.
• The relevant test statistic for the specified number of forecasts.
• Level of confidence of the forecasted values.
• Test statistic times the standard errors of the forecasted values.
• Confidence intervals for the forecasted values, their means, and their expected values.
• Analysis Of Variance Table. This option allows you to calculate an analysis of variance table for the model being estimated. This table contains:

• Regression, residual, and total sums of squares in the model being estimated along with their respective degrees of freedom.
• Regression and residual mean squares.
• F statistic, along with its degrees of freedom and probability value, for the null hypothesis that the coefficients of all variables other than the constant term are zero are also given.
• Test For Reduced Model. This option allows you to test hypotheses on subsets of variables in the model being estimated. When this option is executed you are prompted to choose between dropping variables from the model or specifying a set of constraints on the coefficients of the model. The output includes:

• Error sums of squares for the full and reduced models.
• F statistic and its p-value for the hypothesis that the constraints hold for the model.
• Test For Linear Fit. This option allows you to test the model being estimated for linearity. The output from this option includes:

• Regression, lack of fit, and pure error sums of squares, degrees of freedom, and mean squares.
• F statistic along with its degrees of freedom and p-value, for the null hypothesis that coefficient of determination is equal to zero is also included as is the F statistic for the null hypothesis that the true model being estimated is a linear function of the variables included in the model.
• Variance Inflation Factors. This option allows you to list the variance inflation factors for the coefficients of the model being estimated.

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