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Statistica Textbook Examples
Computer-Aided Multivariate Analysis, Afifi, Clark and May
Chapter 7: Multiple regression and correlation

Page 126 Regression from chapter 6

File
  Open - open the lung data set
Statistics
  Advanced linear/non-linear models
    General regression models
      Simple regression
        OK
          "Quick" tab
            Variables - select ffev1a as the dependent variable and fheight 
            as the independent variable
              OK
                OK
RESULTS
  "Quick" tab
    Coefficients
Parameter Estimates Sigma-restricted parameterization
  FFEV1a Param. FFEV1a Std.Err FFEV1a t FFEV1a p -95% Cnf.Lmt +95% Cnf.Lmt FFEV1a Beta FFEV1a St.Err. -95% Cnf.Lmt +95% Cnf.Lmt
Intercept -4.08670 1.151979 -3.54755 0.000521 -6.36316 -1.81025        
FHEIGHT 0.11811 0.016619 7.10647 0.000000 0.08526 0.15095 0.504396 0.070977 0.364137 0.644655

Page 128 Descriptive statistics 

Statistics
  Basic Statistics
    Descriptive Statistics
      OK
        Variables - select fage, fheight and ffev1a
          OK
            Summary
Descriptive Statistics
  Valid N Mean Minimum Maximum Std.Dev.
FAGE 150 40.13333 26.00000 59.00000 6.889995
FHEIGHT 150 69.26000 61.00000 76.00000 2.779189
FFEV1a 150 4.09327 2.50000 5.85000 0.650752

Page 133 Covariance and correlation matrices

Statistics
  Advanced linear/non-linear models
    General regression models
      Multiple regression
        OK
          "Quick" tab
            Variables - select ffev1a as the dependent variable and fage, fheight 
            and fweight as the independent variables
              OK
RESULTS
  "Matrix" tab
    Covariance
Variance/Covariance Matrix Variances and covariances for the vectors in the design matrix X
  Level Column Effect Col. 1 Col. 2 Col. 3 Col. 4 Col. 5
Intercept   1 Fixed          
FAGE   2 Fixed   47.47 -1.08 -3.6 -1.39
FHEIGHT   3 Fixed   -1.08 7.72 34.7 0.91
FWEIGHT   4 Fixed   -3.65 34.70 573.8 2.07
FFEV1a   5     -1.39 0.91 2.1 0.42

     Correlation (page 134)

Correlations of Vectors in Design Matrix X Correlation matrix for the vectors in the design matrix X
  Level Column Effect Col. 1 Col. 2 Col. 3 Col. 4 Col. 5
Intercept   1 Fixed          
FAGE   2 Fixed   1.00 -0.06 -0.02 -0.31
FHEIGHT   3 Fixed   -0.06 1.00 0.52 0.50
FWEIGHT   4 Fixed   -0.02 0.52 1.00 0.13
FFEV1a   5     -0.31 0.50 0.13 1.00

NOTE:  We reduced the number of decimal places displayed by highlighting all of the cells and clicking on the .00 -> .0 button on the menu bar at the top until only two decimal places were displayed.

Page 138 Table 7.1  ANOVA example from the lung function data (fathers)

Statistics
  Multiple regression
    "Quick" tab
      Variables - select ffev1a as the dependent variable and fage and fheight 
      as the independent variables
        OK
          OK
RESULTS
  "Advanced" tab
    ANOVA (Overall goodness of fit)
Analysis of Variance; DV: FFEV1a
  Sums of Squares df Mean Squares F p-level
Regress. 21.0570 2 10.5285 36.81 0.00
Residual 42.0413 147 0.2860    
Total 63.0983        

Page 140 The t-test at the top

From the results of the ANOVA shown above:

RESULTS
  "Advanced" tab
    Summary: regression results
Regression Summary for Dependent Variable: FFEV1a R= .57768235 R2= .33371690 Adjusted R2= .32465182 F(2,147)=36.813 p<.00000 Std.Error of estimate: .53479
  Beta Std.Err. of Beta B Std.Err. of B t(147) p-level
Intercept     -2.76075 1.137746 -2.42651 0.016456
FAGE -0.282050 0.067431 -0.02664 0.006369 -4.18283 0.000049
FHEIGHT 0.488559 0.067431 0.11440 0.015789 7.24537 0.000000

Page 150 Table 7.5  Statistical output for the lung function data for males and females.

NOTE:  To do this part of the table, you need to combine the fathers' and mothers' data into one column for each of the variables in the equation.  It is easiest to do this via cut-and-paste (just pasting the mothers' data for age under the fathers' age data, for example).

Statistics
  Multiple regression
    "Quick" tab
      Variables - select fev1_all as the dependent variable and age_all and height_all 
      as the independent variables
        OK
          OK
RESULTS
  "Residuals/assumptions/prediction" tab
    Means and standard deviations
Means and Standard Deviations (lung75.sta)
  Means Std.Dev. N
AGE_all 38.84667 6.912484 300
HEIGHT_all 66.67667 3.685657 300
FEV1_all 3.53320 0.802586 300 
    Summary: regression results
Regression Summary for Dependent Variable: FEV1_all (lung75.sta) R= .75557598 R2= .57089506 Adjusted R2= .56800547 F(2,297)=197.57 p<0.0000 Std.Error of estimate: .52751
  Beta Std.Err. of Beta B Std.Err. of B t(297) p-level
Intercept     -6.73699 0.563289 -11.9601 0.00000
AGE_all -0.160178 0.038266 -0.01860 0.004443 -4.1860 0.00004
HEIGHT_all 0.757098 0.038266 0.16486 0.008333 19.7853 0.00000

The second and third panels of the table can be made with the data set that we have for all other parts of this chapter and by following the same steps as those used to generate the output above.

Fathers:

Means and Standard Deviations (lung.sta)
  Means Std.Dev. N
FAGE 40.13333 6.889995 150
FHEIGHT 69.26000 2.779189 150
FFEV1a 4.09327 0.650752 150

Regression Summary for Dependent Variable: FFEV1a (lung.sta) R= .57768235 R2= .33371690 Adjusted R2= .32465182 F(2,147)=36.813 p<.00000 Std.Error of estimate: .53479
  Beta Std.Err. of Beta B Std.Err. of B t(147) p-level
Intercept     -2.76075 1.137746 -2.42651 0.016456
FAGE -0.282050 0.067431 -0.02664 0.006369 -4.18283 0.000049
FHEIGHT 0.488559 0.067431 0.11440 0.015789 7.24537 0.000000

Mothers:

Means and Standard Deviations (lung.sta)
  Means Std.Dev. N
MAGE 37.56000 6.714184 150
MHEIGHT 64.09333 2.469537 150
MFEV1a 2.97313 0.487414 150

Regression Summary for Dependent Variable: MFEV1a (lung.sta) R= .53990588 R2= .29149836 Adjusted R2= .28185889 F(2,147)=30.240 p<.00000 Std.Error of estimate: .41305
  Beta Std.Err. of Beta B Std.Err. of B t(147) p-level
Intercept     -2.21116 0.896067 -2.46763 0.014749
MAGE -0.275164 0.069434 -0.01998 0.005041 -3.96296 0.000115
MHEIGHT 0.469131 0.069434 0.09259 0.013704 6.75651 0.000000

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