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4-1
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COV(XY)XYD(X)D(Y)XY
ρrρ
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r
–1 ≤ r ≤ 10 < r ≤ 1XY–1 ≤ r < 0XY
r = 1XYr = –1XYr = 0
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r
–1 < r < 1| r | ≥ 0.80.5 ≤ | r | < 0.80.3 ≤ | r | <0.5| r | < 0.3
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1)
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2)
3) pp < H0p H0
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2)
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()x1
()x2
()x3
()x4
()x5
1
0.9
67.3
6.8
5
51.9
2
1.1
111.3
19.8
16
90.9
3
4.8
173.0
7.7
17
73.7
4
3.2
80.8
7.2
10
14.5
5
7.8
199.7
16.5
19
63.2
2) “Analyze”→“Scatter Plot (Y X)”
3) “Scatter Plot (Y X)”YYXx1x2x3x4
4) “OK”
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2) “Analyze”→“Multivariate (Y X)”
3) “Multivariate (Y X)”YYXx1x2x3x4
4) “OK”
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p
Yx1Yx1
1) “”Mylib.jyzk
2) “Statistics”→“Descriptive”→“Correlations”“Correlations”4-8
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Yx3x2Yx1x4x5Yx6
(Y)(x3)(x2)(x6)(x5)0p < = 0.05(Y)(x1)(x4)0
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3.
“Scatter Plots”“Confidence ellipseYX1”“Confidence ellipseYX6”4-10
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4-10(Y)(x3)(x4)
“”ε0
k = 1
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01…k N(02)
nxi1xi2…xikyii = 12…n
12…nN(02)
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1…kY
εY2
error sum of squares
YX1X2…Xky1y2…ynSSE = 0SSE
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model sum of squares
X1X2…Xky1y2…ynSSM = 0i = 12 nX1X2…Xk1 = … = k = 0
total sum of squares
y1y2…yn
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SST = SSM + SSESSMy1y2…ynYX1X2…Xk
determination coefficient
R
AdjR2 =
AdjR2
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SASSSTSum of SquaresMean SquareFF0F Statp = P{F F0}
pH0YX1X2…XkH0YX1X2…Xk
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H0(i) i = 0 H1(i)i 0 i = 12…k


H0(i)
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tiFiti0Fi0
piH0(i)i0XiYi0XiYi
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(i12…n)
2n (i12…n)
(i12…n)68(–11)87(–1.51.5)95(–22) i(i12…n).
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2) yi Xjj = 12…k
1 2…nN(01)–2+24-11

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TOL(i) = (1 – R2(i))XiToleranceVIF(i) = ciiVIF(i) = 1/TOL(i)
R(i)XiR(i)1TOL(i)0VIF(i)R(i)0VIF(i)TOL(i)1
VIF(i) > 10
nk
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1) INSIGHTMylib.bldk“Analyze”→“Fit(Y X)”“Fit(Y X)”
2) “Fit(Y X)”Yx1
3) “OK”
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4-15Mean of ResponseYRoot MSEεY
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R_YP_YDistribution(Y)
1) “Analyze”→“Distribution (Y)”“Distribution (Y)”BLDKR_Y“Y”R_Y
2) “OK”
4) “Test for Distribution”“OK”
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Test for Distribution4-20p0.05
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2) YP_Y1002.96
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“OK”
x1
“Curves”→“Test for Distribution”4-24p>.15>0.05

1) “Analyze”→“Fit(Y X)”“Fit(Y X)”
2) “Fit(Y X)”Y“Y”Yx1x2x3x4“X”x1x2x3x4
3) “OK”
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Adj R-SqR2Adj R-Sq0.75710.6991Y
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ToleranceVIF
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x24-32
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4-33
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1.
(1)
“Statistics”→“Regression”→“Linear”“Linear Regression”4-34
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(2)
“Linear Regression”“Plots”“Linear RegressionPlots”“Predicted”“Plot observed vs independent”“OK”Yx24-36
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(3)
“Linear Regression”“Model”“Linear RegressionModel”“Do not include an intercept”4-37
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tx20
1) “Statistics” → “Regression” → “Linear”“Linear Regression”
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6x1x4x5x6
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(2)
“”“Linear Regression”“Model”“Linear RegressionModel”
“Method”“Backward elimination”4-41
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VAR <>
RUN
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PRINTMODEL
MODBL“SELECTION = ”NONEFORWARDBACKWARDSTEPWISEMAXRR2MINRR2RSQUARER2ADJRSQR2CPMallowsCp
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run;
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print cli;
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y()x1x2x3x4x1 = x3 – x4x1x2y
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plot y*x1=1 y*x2=2;
symbol1 v=star i=rl cv=orange ci=blue w=1;
symbol2 v=star i=rq cv=orange ci=blue w=1;
run;
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(2)
print cli;
1) R2 = 0.9054y()90.54FFp<0.0001(3)
2) (3)01230 = 17.32441 = 1.30702 = -3.69563 = 0.34862tp = 0.05640.05
(4)
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(5)
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print cli;
(6)
(6)x1 = 0.2x2 = 6.5y
= 29.1133 + 11.1342 0.2 – 7.6080 6.5 + 0.6712 6.52 – 1.4777 0.2 6.5 = 8.3272()
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2) “Analyze”→“Scatter Plot(Y X)”
3) “Scatter Plot(Y X)”YYXX“OK”YX4-58
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INSIGHTMylib.gbzl“Edit”→“Variables”→“Other”“Edit Variables”4-59 4-60
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4-62
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4-63
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4-64
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