42 SPSS UPDATE 7-9 | 4

MANOVA also prints multivariate significance tests of the hypothesis that the regression
| coefficients are zero, under the heading EFFECT..WITHIN CELLS REGRESSION. (WITHIN ;
CELLS indicates that the within-cells error matrix was used in the model.) These tests for the :
dental calculus data of Figure 1.37a are shown in Figure 1.37c. (See Section 1.38 for a more
detailed discussion of regression analysis.)

Figure 1.37€ j

EFFECT .. WITHIN CELI.S REGRESSION s si
MULTIVARIATE TESTS OF SIGNIFICANCE (S - 1, M Il/2. N 47? 1/2)

TEST NAME VALJE APPROX. F HYPOTH. DF ERROR DF SIG. OF F :
PILLAIS 72613 85 .72625 3.00 97.00 0.0 k
HOTELLINGS 2.65133 85 ..72625 3.00 ' 97.00 0.0 a
WILKS 271387 85.72625 3.00 97.00 0.0 E
ROYS . 72613

EIGENVALUES AND CANONICAL. CORRELATIONS
ROOT NO. EIGENVALVE PCT. CUM. PCT. CANON. COR.  SOUARED COR.

1 2.65133 100 .00000 100.00000 .85213 .T2613
DIMENSION REDUCTION ANALYSIS
ROOTS WILKS LAMBDA F HYPOTH. DF ERROR DF SIG. OF F
1 TO 1 27387 85..72625 3.00 97.00 0.0

UNIVARIATE F-TESTS WITH (1.99) D. F.
VARIABLE SO. MUL. R MUL. R ADJ. R-SO. HYPOTH MS ERROR MS F SIG. OF F

sd
RCAN -13468 36699 -07350 18.57190 1.20529 15.40872 -000
RLI »41804 .64656 37689 109.47447 1.53939 T1.11537 -000
RCI -T0832 84162 68770 300.31570 1.24914 240.41814 0.0

A a A NEM NA IRENE ERI ENNNO]

The estimated parameters for the regression of each response variable on the covariate are
also listed, together with standard errors, t-values, and confidence intervals. For Figure 1.37a, the
results in Figure 1.37d were obtained.

Figure 1.37d

o ME VENE 7 ANEJ: NE TEV VE O ET O EP PON
REGRESSION ANALYSIS FOR WITHIN CELLS ERROR TERM

DEPENDENT VARIABLE ..RCAN

| COVARIATE B BETA STD. ERR. T-VALUE SIG. OF T LOWER .95 CL UPPER .95 CL
LCI .1731949251  .3669895761 .04412 3.92539 .000 .08565 .26074
DEPENDENT VARIABLE ..RLI .
COVARIATE B BETA STD. ERR. T-VALVE SIG. OF T LOWER .95 CL UPPER .95 CL
LCI . 4204974555 6465616861 .04986 8.43299 0.0 | .32156 51944
DEPENDENT VARIABLE ..RCI

COVARIATE B BETA STD. ERR. T-VALUE SIG. OF T LOWER .95 CL UPPER .95 CL
LCI .6964596479 8416200881 .04492 15.50542 o.o .60733 .T8559

1.38 MULTIVARIATE MULTIPLE LINEAR REGRESSION

1.39 The Multivariate Linear Regression Model

The univariate regression model
Y, < Bo t BiXa t... t BoXp bt €;

expresses the ith observation of the dependent variable Y as a linear function of p independent
variables X, and the error term €;.