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Y = [98, 112.5, 84, 102.5, 102.5, 50.5, 90, 77, 112, 150, 128, 133, 85, 112];
X = [65.3, 69, 56.5, 62.8, 63.5, 51.3, 64.3, 56.3, 66.5, 72, 64.8, 67, 57.5, 66.5];
X = J( N Row( X ), 1 ) || X; // put in an intercept column of 1s
beta = Inv( X` * X ) * X` * Y; // the least square estimates
resid = Y - X * beta; // the residuals, Y - predicted
sse = resid` * resid; // sum of squared errors
Show( beta, sse );
// open the data table
dt = Open( "$SAMPLE_DATA/Big Class.jmp" );
 
// get data into matrices
x = (Column( "Age" ) << Get Values ) || (Column( "Height" ) << Get Values);
x = J(N Row( x ), 1, 1) || x;
y = Column( "Weight" ) << Get Values;
 
// regression calculations
xpxi = Inv( x` * x );
beta = xpxi * x` * y; // parameter estimates
resid = y - x * beta; // residuals
sse = resid` * resid; // sum of squared errors
dfe = N Row( x ) - N Col( x );  // degrees of freedom
mse = sse / dfe; // mean square error, error variance estimate
 
// additional calculations on estimates
stdb = Sqrt( Vec Diag( xpxi ) * mse ); // standard errors of estimates
alpha = .05;
qt = Students t Quantile( 1 - alpha / 2, dfe );
betau95 = beta + qt * stdb; // upper 95% confidence limits
betal95 = beta - qt * stdb; // lower 95% confidence limits
tratio = beta :/ stdb; // Student's T ratios
probt = ( 1 - TDistribution( Abs( tratio ), dfe ) ) * 2; // p-values
 
// present results
New Window( "Big Class Regression",
	Table Box(
		String Col Box( "Term",{"Intercept", "Age", "Height"} ),
		Number Col Box( "Estimate", beta ),
		Number Col Box( "Std Error", stdb ),
		Number Col Box( "TRatio", tratio ),
		Number Col Box( "Prob>|t|", probt ),
		Number Col Box( "Lower95%", betal95 ),
		Number Col Box( "Upper95%", betau95 ) ) );
Y = a + bX + e
Y is a vector of responses
a is the intercept term
b is a vector of coefficients
X is a design matrix for the factor
e is an error term
factor = [1, 2, 3, 1, 2, 3, 1, 2, 3];
y = [1, 2, 3, 4, 3, 2, 5, 4, 3];
Design Nom( factor );
[1 0, 0 1, -1 -1, 1 0, 0 1, -1 -1, 1 0, 0 1, -1 -1]
x = J( 9, 1, 1) || Design Nom( factor );
[1 1 0,
1 0 1,
1 -1 -1,
1 1 0,
1 0 1,
1 -1 -1,
1 1 0,
1 0 1,
1 -1 -1]
You can construct matrix M in one step by concatenating the pieces, as follows:
M = ( x` * x || x` * y )
        |/
  ( y` * x || y` * y );
[9 0 0 27,
	0 6 3 2,
	0 3 6 1,
	27 2 1 93]
Now, sweep M over all the columns in XX for the full fit model, and over the first column only for the intercept-only model:
FullFit = Sweep( M, [1, 2, 3] ); // full fit model
InterceptOnly = Sweep( M, [1] ); // model with intercept only
[0.111111111111111 0 0 3,
0 0.222222222222222 -0.11111111111111 0.333333333333333,
0 -0.11111111111111 0.222222222222222 0,
-3 -0.33333333333333 0 11.33333333333333]
Because of the use of Design Nom(), the coefficient for the third level is the difference, –0.333.
Figure 7.1 ANOVA Report Within Fit Model
dt = New Table( "Data" );
dt << New Column( "y", Set Values( [1, 2, 3, 4, 3, 2, 5, 4, 3] ) );
dt << New Column( "factor", "Nominal", Values( [1, 2, 3, 1, 2, 3, 1, 2, 3] ) );
obj = Fit Model(
	Y( :y ),
	Effects( :factor ),
	Personality( "Standard Least Squares" ),
	Run(
		y << {Plot Actual by Predicted( 0 ), Plot Residual by Predicted( 0 ),
		Plot Effect Leverage( 0 )}
	)
);
ranova = obj << Report;
ranova[Outline Box( 6 )] << Close( 0 );
ranova[Outline Box( 7 )] << Close( 1 );
ranova[Outline Box( 9 )] << Close( 1 );
ranova[Outline Box( 5 ), Number Col Box( 2 )] << Select;
ranova[Outline Box( 6 ), Number Col Box( 1 )] << Select;

Help created on 3/19/2020