第 2 章 一元线性回归
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第 2 章 一元线性回归. 2 .1 一元线性回归模型 2 .2 参数 的估计 2 .3 最小二乘估计的性质 2 .4 回归方程的显著性检验 2 .5 残差分析 2 .6 回归系数的区间估计 2 .7 预测和控制 2 .8 本章小结与评注. 2 .1 一元线性回归模型. 表 2.1 火灾损失表. 例 2 .1 表 2.1 列出了 15 起火灾事故的损失及火灾发生地与最近的消防站的距离。. 2 .1 一元线性回归模型. 表 2.2 人均国民收入表. - PowerPoint PPT PresentationTRANSCRIPT
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2 2 .1 2 .2 2 .3 2 .4 2 .5 2 .6 2 .7 2 .8
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2 .1 2 .1 2.115 2.1
x(km)
3.4
1.8
4.6
2.3
3.1
5.5
0.7
3.0
y()
26.2
17.8
31.3
23.1
27.5
36.0
14.1
22.3
x(km)
2.6
4.3
2.1
1.1
6.1
4.8
3.8
y()
19.6
31.3
24.0
17.3
43.2
36.4
26.1
Chart1
26.2
17.8
31.3
23.1
27.5
36
14.1
22.3
19.6
31.3
24
17.3
43.2
36.4
26.1
x(km)
y()
p19-2.1
Sheet1
3.426.2
1.817.8
4.631.3
2.323.1
3.127.5
5.536
0.714.1
322.3
2.619.6
4.331.3
2.124
1.117.3
6.143.2
4.836.4
3.826.1
Sheet1
x(km)
y()
p19-2.1
Sheet2
Sheet3
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2 .1 2.2 y(); x() 2.2
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
460
489
525
580
692
853
956
1104
1355
1512
234.75
259.26
280.58
305.97
347.15
433.53
481.36
545.40
687.51
756.27
1990
1991
1992
1993
1994
1995
1996
1997
1998
1634
1879
2287
2939
3923
4854
5576
6053
6392
797.08
890.66
1063.39
1323.22
1736.32
2224.59
2627.06
2819.36
2958.18
-
2 .1
Chart1
234.751
259.26
280.58
305.97
347.15
433.53
481.36
545.4
687.51
756.27
797.08
890.66
1063.39
1323.22
1736.32
2224.59
2627.06
2819.36
2958.18
p19-2.2
Sheet1
460234.75
489259.26
525280.58
580305.97
692347.15
853433.53
956481.36
1104545.4
1355687.51
1512756.27
1634797.08
1879890.66
22871063.39
29391323.22
39231736.32
48542224.59
55762627.06
60532819.36
63922958.18
Sheet1
1
p19-2.2
Sheet2
Sheet3
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2 .1
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2 .1 (x1y1),(x2y2),,(xnyn)
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2 .2 01 (Ordinary Least Square Estimation,OLSE) 01yi, yi
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2 .2 01
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2 .2 01,
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2 .2 01OLSE
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2 .2 2.1
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2 .2
iN(0,2),2.10yi:
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2 .2 01 y1,y2,,yn
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2 .3 y1,y2,,yn
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2 .3
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2 .3
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2 .3
GaussMarkov
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2.4 t H0 1=0 H1 10 H0 1=0
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2.4 t t
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2.4 12.1 Excel
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P ?(P-value)P Significence Probability Value ()
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P / 2 / 2 tH01/2 P 1/2 P
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P H0a1 - P
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P H0a1 - P
-
P
p- , H0p- , H0
p- =2p-
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2.4 2. 2.1SPSS
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2.4 2.SPSS
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2.4 F SST = SSR + SSEF
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2.4 F
FP
1
n-2
n-1SSR
SSE
SSTSSR/1
SSE/n-2P(F>F)=P
-
2.4
-
2.4
-
2.4 1 =0
n-25%1%n-25%1%n-25%1%10.9971.000160.4680.590350.3250.41820.9500.990170.4560.575400.3040.39330.8780.959180.4440.561450.2880.37240.8110.947190.4330.549500.2730.35450.7540.874200.4230.537600.2500.32560.7070.834210.4130.526700.2320.30270.6660.798220.4040.515800.2170.28380.6320.765230.3960.505900.2050.26790.6020.735240.3880.4961000.1950.254100.5760.708250.3810.4871250.1740.228110.5530.684260.3740.4781500.1590.208120.5320.661270.3670.4702000.1380.181130.5140.641280.3610.4633000.1130.148140.4970.623290.3550.4564000.0980.128150.4820.606300.3490.44910000.0620.081
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2.4 SPSS
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2.4 |r|0.80.5|r| 0.80.3|r| 0.5|r| 0.3
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2.4 H0: b=0H0: r=0H0:
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2.4
-
2.5 eiei
-
2.5
-
2.5 2.6
-
2.5 1 E (ei)=0 :
-
2.5 2
-
2.5
4
3
5
4
6
7
9
8
7
10
11
10
20
x
y
Sheet1
93SUMMARY OUTPUT
135
154
176Multiple R0.9606874187
187R Square0.9229203165
269Adjusted R Square0.9152123481
2282.1028087196
20712
2310
2811
3010dfSSMSFSignificance F
50201529.4486215539529.4486215539119.7358725840.0000006922
1044.21804511284.4218045113
11573.6666666667
Coefficientst StatP-valueLower 95%Upper 95% 95.0% 95.0%
Intercept2.43233082711.81651591191.33900881960.2102086799-1.61511955196.479781206-1.61511955196.479781206
X Variable 12.44360902260.223315865310.9423887970.00000069221.94603018072.94118786441.94603018072.9411878644
Sheet1
0
0
0
0
0
0
0
0
0
0
0
0
x
y
11-13
Sheet2
SUMMARY OUTPUT
Multiple R0.960687
R Square0.922920
Adjusted R Square0.915212
2.102809
12
dfSSMSFSignificance F
1529.448622529.448622119.7358725840.0000006922
1044.2180454.421805
11573.666667
Coefficientst StatP-value 95.0% 95.0%
Intercept2.4323311.8165161.3390090.210209-1.6151206.479781
X Variable 12.4436090.22331610.9423890.0000011.9460302.941188
Sheet3
MBD00013710.unknown
MBD00013713.unknown
MBD00013715.unknown
MBD00013711.unknown
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2.5 3. :
-
2.5
-
2.6 11-
-
2.7
-
2.7 T1,T2 1
-
1.
-
1.
-
y01- y095% 1.
-
E(y0)1- E(y0)=0+1x01.
-
2.1x0=3.5
95% 22.3232.67 E(y0)26.1928.80 95% =27.50-22.31627.50+22.316=22.8732.13
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y(T1, T2),x1- x=0.05,
-
2.8 2.2 y(); x()2.2
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
460
489
525
580
692
853
956
1104
1355
1512
234.75
259.26
280.58
305.97
347.15
433.53
481.36
545.40
687.51
756.27
1990
1991
1992
1993
1994
1995
1996
1997
1998
1634
1879
2287
2939
3923
4854
5576
6053
6392
797.08
890.66
1063.39
1323.22
1736.32
2224.59
2627.06
2819.36
2958.18
-
2.8 1973Anscombe, ,,F,
x
y
x
y
x
y
x
y
4
4.26
4
3.1
4
5.39
8
6.58
5
5.68
5
4.74
5
5.73
8
5.76
6
7.24
6
6.13
6
6.08
8
7.71
7
4.82
7
7.26
7
6.44
8
8.84
8
6.95
8
8.14
8
6.77
8
8.47
9
8.81
9
8.77
9
7.11
8
7.04
10
8.04
10
9.14
10
7.46
8
5.25
11
8.33
11
9.26
11
7.81
8
5.56
12
10.84
12
9.13
12
8.15
8
7.91
13
7.58
13
8.74
13
12.74
8
6.89
14
9.96
14
8.1
14
8.84
19
12.5
-
2.8
Rejection region does NOT include critical value.Rejection region does NOT include critical value.