Tam Logaritmik FonksiyonTam Logaritmik Fonksiyon
X3
X2
Y1
Y2
0<2<1
2<0
Y
X2
2>1
(X3 sabit tutulduğunda)
uk321 e.XX.X.Y k32
lnY =ln1 + 2 lnX2+ 3 lnX3 + ... + k lnXk + u lne
Y* =1 *+ 2 X2
*+ 3 X3* + ... + k Xk
* + u
2*2
*1
***
*2
*1
*
Xb̂b̂XXY
Xb̂b̂nY
eXb̂b̂Y *2
*1
*
?b̂*1 ?b̂2
Tam Logaritmik FonksiyonTam Logaritmik Fonksiyon
Y
X
X
1Y.2
2X.Y 1
121
2X..'Y X
1X.. 2
12
X
1Y.2
Y
X
X
YEyx
2
rsapmasızdı i tahminlerb̂ veb̂ 2*1
.sapmalıdır tahminib̂logantib *11
aynıdır. heryerindeeğrinin tahminib̂ 2
Tam Logaritmik FonksiyonTam Logaritmik Fonksiyon
Uygulama 4.3 (207-210)Uygulama 4.3 (207-210)
X
4003002001000
Y 80
60
40
20
0
Uygulama 4.3 (207-210)Uygulama 4.3 (207-210)
Uygulama 4.3 (207-210)Uygulama 4.3 (207-210)
*Y n
Y*25
1449.101 = 4.0458
*Xn
X*25
0374.124 = 4.9615
x*2 =7.3986
y*x* =2.6911
Uygulama 4.3 (207-210)Uygulama 4.3 (207-210)
2*
**
2 x
yxb̂
7.3986
2.6911
= 2.2413= 4.0458 - (0.3637) 4.9615
[ln(9.4046) = 2.2413]
= 0.3637
Uygulama 4.3 (207-210)Uygulama 4.3 (207-210)
Üretim FonksiyonuÜretim Fonksiyonu
32 b3
b21 X.XbY Y= Üretim X2=Emek ; X3=Sermaye
22
2 X
Yb
X
Y
= Emeğin Marjinal Verimliliği
33
3 X
Yb
X
Y
= Sermayenin Marjinal Verimliliği
lnY = -3.4485 + 1.5255 lnX2 + 0.4858 lnX3
(t) (-1.43) (2.87) (4.82)
n=15 Düz-R2= 0.8738
Yarı-Logaritmik FonksiyonYarı-Logaritmik FonksiyonLog-Doğ Model(Üstel Model)Log-Doğ Model(Üstel Model)
Y
X(a)
Y = Aeb X2
Y
X(b)
Y = Aeb X2
A
A
b >0
b <02
2
Xbb 21eY Xbb 21ee Xb2e A
Yarı-Logaritmik FonksiyonYarı-Logaritmik FonksiyonLog-Doğ Model(Üstel Model)Log-Doğ Model(Üstel Model)
lnY = b1 +b2 X+ u
X d
Yln db2
X d
Y d.
Y
1
X d
Y/Y d
değişmemutlak dekiX'
değişme nisbi dekiY'
Y
X
X d
Y dEyx = ( b2Y )
Y
X= b2 X
Artış Hızı ModeliArtış Hızı ModeliLog-Doğ Model(Üstel Model)Log-Doğ Model(Üstel Model)
lnY = b1 +b2 t + u
r = (Antilog b2 - 1) . 100
Y= İş hacmi(1983-1988)
r = (Antilog 0.131 - 1) . 100
= (1.13997 - 1) . 100
= (0.13997 1) . 100
= % 14
Ücret ModeliÜcret ModeliLog-Doğ Model(Üstel Model)Log-Doğ Model(Üstel Model)
lnY = 1.19 + 0.033 X2 + 0.074 X3
Aşağıdaki ücret modeli Uygulama 9.3’den alınmıştır.(s.427)
Modelde:
Y:Haftalık Kazanç ($) ; X2: Tecrübe ; X3 : Eğitim Kategorisi
Yarı-Logaritmik Fonksiyon Yarı-Logaritmik Fonksiyon Doğ - Log ModelDoğ - Log Model
Y = b1 +b2 lnX+ u
Y
X(a)
Y = b + b lnX
Y
X(b)
b >0
b <02
2
21 Y = b + b lnX21
Yarı-Logaritmik Fonksiyon Yarı-Logaritmik Fonksiyon Doğ - Log ModelDoğ - Log Model
Y = b1 +b2 lnX+ u
lnX d
dYb2
)X/1(
1
X d
Y d
X/X d
Y d
değişme nisbi dekiX'
değişmemutlak dekiY'
Y
X
X d
Y dEyx
Y
X
X
b2 Y
b2
Hedonik Model Hedonik Model Doğ - Log ModelDoğ - Log Model
Y = b1 +b2 lnX2+ b3 lnX3 + u
Fiyat = -1.749.97 + 299.97 ln(m2) - 145.09 ln(YatakOda)
(t) (-6.8) (7.5) (-1.7)
Prob. [0.1148]
Düz-R2= 0.826 sd=11
Polinomial Fonksiyonlar Polinomial Fonksiyonlar
Y =1 + 2 X + 3 X2 + 4 X3 + ... + k+1 Xk + u
Kuadratik Model:
Y =1 + 2 X + 3 X2 + u
dX
dY= 2 + 23 X =
X0= -2 / 23
Xd
Yd2
2
= 23
Eğer 3<0 ise X0 noktası maksimumdur
Eğer 3>0 ise X0 noktası minimumdur
Polinomial Fonksiyonlar Polinomial Fonksiyonlar Kuadratik ModelKuadratik Model
OM = 10.52 - 0.175 Çıktı + 0.0009 (Çıktı)2 + 0.02 GMİ
(t) (14.3) (-9.7) (7.8) (14.45)
Düz-R2=0.978 sd=16
OM= Ortalama Maliyet ; Çıktı =Üretimİndeksi
GMİ= Girdi Maliyetleri İndeksi
Polinomial Fonksiyonlar Polinomial Fonksiyonlar Kübik ModelKübik Model
TM= Toplam Maliyet ;Q =Üretim Miktarı
Polinomial Fonksiyonlar Polinomial Fonksiyonlar Kübik ModelKübik Model
Y =1 + 2 X + 3 X2 + 4 X3 + u
TM = 141.76 + 63.47 Q - 12.96 Q2 + 0.94 Q3
s(bi) (6.37) (4.78) (0.98) (0.059)
R2 =0.998 sd=6
DATA4-1: Data on single family homes in University City community of San Diego, in 1990.
price = sale price in thousands of dollars (Range 199.9 - 505)
sqft = square feet of living area (Range 1065 - 3000)
bedrms = number of bedrooms (Range 3 - 4)
baths = number of bath roooms (Range 1.75 - 3)
Dependent Variable: PRICE Included observations: 14
Variable Coefficient Std. Error t-Statistic Prob.
C 52.35091 37.28549 1.404056 0.1857
SQFT 0.138750 0.018733 7.406788 0.0000
R-squared 0.820522 Akaike info criterion 10.29774
Adjusted R-squared 0.805565 Schwarz criterion 10.38904
S.E. of regression 39.02304 F-statistic 54.86051
Sum squared resid 18273.57 Prob(F-statistic) 0.000008
Dependent Variable: PRICE Included observations: 14
Variable Coefficient Std. Error t-Statistic Prob.
C -1749.974 259.1410 -6.752980 0.0000
LOG(SQFT) 299.9724 39.97577 7.503856 0.0000
LOG(BEDRMS) -145.0942 84.71878 -1.712657 0.1148
R-squared 0.852853 Akaike info criterion 10.24198
Adjusted R-squared 0.826099 Schwarz criterion 10.37892
S.E. of regression 36.90497 F-statistic 31.87767
Sum squared resid 14981.74 Prob(F-statistic) 0.000026
Dependent Variable: PRICE Included observations: 14
Variable Coefficient Std. Error t-Statistic Prob.
C -28.60714 133.0212 -0.215057 0.8337
SQFT 0.224620 0.136493 1.645651 0.1281
SQFT*SQFT -2.10E-05 3.30E-05 -0.635444 0.5381
R-squared 0.826877 Mean dependent var 317.4929
Adjusted R-squared 0.795400 S.D. dependent var 88.49816
S.E. of regression 40.03014 Akaike info criterion 10.40455
Sum squared resid 17626.53 Schwarz criterion 10.54149
Log likelihood -69.83186 F-statistic 26.26930
Durbin-Watson stat 1.994036 Prob(F-statistic) 0.000065
Dependent Variable: PRICE Included observations: 14
Variable Coefficient Std. Error t-Statistic Prob.
C -1775.234 383.2026 -4.632625 0.0007
LOG(SQFT) 284.2528 60.41533 4.704979 0.0006
BATHS -18.18913 41.03884 -0.443217 0.6662
R-squared 0.816886 Akaike info criterion 10.46066
Adjusted R-squared 0.783593 Schwarz criterion 10.59760
S.E. of regression 41.16898 F-statistic 24.53596
Sum squared resid 18643.74 Prob(F-statistic) 0.000088
DATA6-1: Data on cost function Source: W.A. Spurr and C.P.Bonini, STATISTICAL ANALYSIS FOR BUSINESS
DECISIONS, Irwin, 1973, Page 535.
UNITCOST = Cost per unit dollars (Range 3.65 - 6.62)
OUTPUT = Index of output (Range 50 - 104)
INPCOST = Index of input costs (Range 80 - 150)
Dependent Variable: UNITCOST Included observations: 20
VariableCoefficien
t Std. Error t-Statistic Prob.
C 10.39073 1.330698 7.808484 0.0000
OUTPUT -0.173953 0.019145 -9.085969 0.0000
OUTPUT*OUTPUT 0.000891 0.000122 7.278983 0.0000
INPCOST 0.022162 0.016613 1.333987 0.2021
INPCOST*INPCOST -8.57E-06 7.11E-05 -0.120474 0.9057
R-squared 0.981884 Akaike info criterion -1.236679
Adjusted R-squared 0.977053 Schwarz criterion -0.987746
S.E. of regression 0.117251 F-statistic 203.2449
Sum squared resid 0.206217 Prob(F-statistic) 0.000000
Dependent Variable: UNITCOST Included observations: 20
Variable Coefficient Std. Error t-Statistic Prob.
C 10.52230 0.736531 14.28630 0.0000
OUTPUT -0.174473 0.018069 -9.655786 0.0000
OUTPUT*OUTPUT 0.000895 0.000115 7.756616 0.0000
INPCOST 0.020168 0.001395 14.45369 0.0000
R-squared 0.981866 Akaike info criterion -1.335712
Adjusted R-squared 0.978466 Schwarz criterion -1.136566
S.E. of regression 0.113583 F-statistic 288.7748
Sum squared resid 0.206417 Prob(F-statistic) 0.000000
d(unit cos t)
d(output)- 0.174473+2*0.000895*Output
= - 0.174473+0.00179*Output
= - 0.174473+0.00179*(1) = - 0.173
0
1
2
3
4
5
6
7
8
40 50 60 70 80 90 100 110
unitcost-tah1 unitcost-tah2 unitcost-tah3
Polinom (unitcost-tah1) Polinom (unitcost-tah2) Polinom (unitcost-tah3)
DATA6-2: Data on the white tuna (Thunnus Alalunga) fishery production in the Basque region of Spain. Data compiled by Felix Telleria.
catch = total catch in thousands of tonnes, Range 16.608 - 51.8
effort = total days of fishing in thousands, Range 10.31185 - 61.24754
Üretim Fonksiyonu Tahmini
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70
CATCH
Üretim Fonksiyonu Tahmini
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70
CATCH Polinom (CATCH)
Dependent Variable: CATCH Sample: 1961 1994
Variable Coefficient Std. Error t-Statistic Prob.
C 2.339564 5.785686 0.404371 0.6887
EFFORT 1.491794 0.383074 3.894275 0.0005
EFFORT*EFFORT -0.014521 0.005386 -2.696384 0.0112
R-squared 0.670780 Mean dependent var 31.83994
Adjusted R-squared 0.649540 S.D. dependent var 9.449949
S.E. of regression 5.594338 Akaike info criterion 6.365484
Sum squared resid 970.1953 Schwarz criterion 6.500163
Log likelihood -105.2132 F-statistic 31.58097
Durbin-Watson stat 1.453119 Prob(F-statistic) 0.000000
Dependent Variable: CATCHSample: 1961 1994
Variable Coefficient Std. Error t-Statistic Prob.
EFFORT 1.641621 0.095991 17.10185 0.0000
EFFORT*EFFORT -0.016530 0.002056 -8.041338 0.0000
R-squared 0.669043 Mean dependent var 31.83994
Adjusted R-squared 0.658701 S.D. dependent var 9.449949
S.E. of regression 5.520736 Akaike info criterion 6.311922
Sum squared resid 975.3128 Schwarz criterion 6.401708
Log likelihood -105.3027 Durbin-Watson stat 1.512102
DATA6-3: United Kingdom Annual data.
Cons = Per capita consumption expenditure in British pounds (Range 1858 - 4744)
DI = Per capita personal disposable income in British pounds (Range 1875 - 5084)
Source: Economic Trends, Annual Supplement 1991 Edition. A publication of the Government Statistical Service, London, UK.
Model A:
Dependent Variable: CONS Sample: 1948 1989
Variable Coefficient Std. Error t-Statistic Prob.
C 168.3149 43.27960 3.889013 0.0004
DI 0.864323 0.013300 64.98492 0.0000
R-squared 0.990617 Mean dependent var 2876.548
Adjusted R-squared 0.990382 S.D. dependent var 771.6100
S.E. of regression 75.67110 Akaike info criterion 11.53712
Sum squared resid 229044.6 Schwarz criterion 11.61986
Log likelihood -240.2795 F-statistic 4223.040
Durbin-Watson stat 0.247444 Prob(F-statistic) 0.000000
Model B:
Dependent Variable: CONS Sample (adjusted): 1949 1989
Variable Coefficient Std. Error t-Statistic Prob.
C -56.09466 29.93634 -1.873798 0.0689
CONS(-1) 1.068312 0.097298 10.97983 0.0000
DI 0.684000 0.084986 8.048355 0.0000
DI(-1) -0.723031 0.080315 -9.002388 0.0000
R-squared 0.998043 Mean dependent var 2901.390
Adjusted R-squared 0.997885 S.D. dependent var 764.0013
S.E. of regression 35.13765 Akaike info criterion 10.04889
Sum squared resid 45682.20 Schwarz criterion 10.21607
Log likelihood -202.0023 F-statistic 6291.164
Durbin-Watson stat 1.595453 Prob(F-statistic) 0.000000
Wald Test:
Null Hypothesis :
C(3)=0
C(4)=0
Test Statistic Value df Probability
F-statistic 48.43943 (2, 37) 0.0000
Chi-square 96.87885 2 0.0000
Model C:
Dependent Variable: CONS Sample (adjusted): 1949 1989
Variable Coefficient Std. Error t-Statistic Prob.
C -46.80204 22.56606 -2.074001 0.0449
CONS(-1) 1.021883 0.008307 123.0201 0.0000
DI-DI(-1) 0.705785 0.071060 9.932268 0.0000
R-squared 0.998031 Mean dependent var 2901.390
Adjusted R-squared 0.997928 S.D. dependent var 764.0013
S.E. of regression 34.77955 Akaike info criterion 10.00629
Sum squared resid 45965.44 Schwarz criterion 10.13167
Log likelihood -202.1290 F-statistic 9631.956
Durbin-Watson stat 1.535694 Prob(F-statistic) 0.000000
-80
-40
0
40
80
1000
2000
3000
4000
5000
1950 1955 1960 1965 1970 1975 1980 1985
Residual Actual Fitted
DATA3-3: Annual data on U.S. Patents and R&D expenditures
YEAR = 1960-93, 34 observations.
PATENTS = Number of patent applications filed, in thousands (Range 84.5 - 189.4)
Source: Statistical Abstract of the U.S., various years.
R&D = R&D expenditures, billions of 1992 dollars obtained as the ratio of expenditure on current dollars divided by the GDP price deflator. (Range 57.94 - 166.7)
Source for R&D expenditures, 1995 Statistical Abstract of the U.S., Table 979, Page 611, and earlier issues Source for GDP deflator, 1996 Economic Report of the President, Table B-3, Page 284.
80
100
120
140
160
180
200
40 60 80 100 120 140 160 180
RD
PATENTS
Dependent Variable: PATENTS Sample: 1960 1993
Variable Coefficient Std. Error t-Statistic Prob.
C 34.57106 6.357873 5.437521 0.0000
RD 0.791935 0.056704 13.96621 0.0000
R-squared 0.859065 Mean dependent var 119.2382
Adjusted R-squared 0.854661 S.D. dependent var 29.30583
S.E. of regression 11.17237 Akaike info criterion 7.721787
Sum squared resid 3994.300 Schwarz criterion 7.811573
Log likelihood -129.2704 F-statistic 195.0551
Durbin-Watson stat 0.233951 Prob(F-statistic) 0.000000
Dependent Variable: PATENTS
Sample (adjusted): 1964 1993
Variable Coefficient Std. Error t-Statistic Prob.
C 85.35255 22.10268 3.861639 0.0011
RD -0.047681 1.125105 -0.042379 0.9666
RDG1 0.603316 2.056192 0.293414 0.7724
RDG2 0.000179 2.185027 8.21E-05 0.9999
RDG3 -0.586882 2.052188 -0.285979 0.7780
RDG4 -0.183709 1.099382 -0.167102 0.8691
RD*RD -0.000733 0.004898 -0.149577 0.8827
RDG1*RDG1 -0.001754 0.008900 -0.197047 0.8459
RDG2*RDG2 0.001736 0.009822 0.176776 0.8616
RDG3*RDG3 -0.000756 0.009238 -0.081882 0.9356
RDG4*RDG4 0.007144 0.005085 1.404834 0.1762
R-squared 0.990710 Mean dependent var 123.3300
Adjusted R-squared 0.985821 S.D. dependent var 28.79514
S.E. of regression 3.428817 Akaike info criterion 5.578882
Sum squared resid 223.3789 Schwarz criterion 6.092655
Log likelihood -72.68324 F-statistic 202.6257
Durbin-Watson stat 1.797425 Prob(F-statistic) 0.000000
Dependent Variable: PATENTS
Sample (adjusted): 1964 1993
Variable Coefficient Std. Error t-Statistic Prob.
C 84.84085 19.05788 4.451746 0.0002
RDG1 0.604292 0.635069 0.951537 0.3517
RDG3 -0.735232 0.523331 -1.404909 0.1740
RDG4 -0.074464 0.513419 -0.145035 0.8860
RD*RD -0.000949 0.001151 -0.824413 0.4186
RDG1*RDG1 -0.001693 0.003414 -0.495939 0.6249
RDG2*RDG2 0.001628 0.002538 0.641485 0.5278
RDG4*RDG4 0.006610 0.001965 3.364449 0.0028
R-squared 0.990700 Mean dependent var 123.3300
Adjusted R-squared 0.987741 S.D. dependent var 28.79514
S.E. of regression 3.188219 Akaike info criterion 5.379980
Sum squared resid 223.6243 Schwarz criterion 5.753633
Log likelihood -72.69970 F-statistic 334.7991
Durbin-Watson stat 1.810383 Prob(F-statistic) 0.000000
Dependent Variable: PATENTS
Sample (adjusted): 1964 1993
Included observations: 30 after adjustments
Variable Coefficient Std. Error t-Statistic Prob.
C 82.85449 12.03555 6.884148 0.0000
RDG1 0.477055 0.327782 1.455404 0.1580
RDG3 -0.637010 0.238843 -2.667066 0.0132
RD*RD -0.001146 0.001000 -1.146413 0.2625
RDG4*RDG4 0.006519 0.000678 9.608783 0.0000
R-squared 0.990289 Mean dependent var 123.3300
Adjusted R-squared 0.988735 S.D. dependent var 28.79514
S.E. of regression 3.056218 Akaike info criterion 5.223245
Sum squared resid 233.5118 Schwarz criterion 5.456778
Log likelihood -73.34868 F-statistic 637.3376
Durbin-Watson stat 1.843677 Prob(F-statistic) 0.000000
Dependent Variable: PATENTS
Sample (adjusted): 1964 1993
Variable Coefficient Std. Error t-Statistic Prob.
C 91.34639 6.404627 14.26256 0.0000
RDG3 -0.295068 0.117463 -2.512013 0.0183
RDG4*RDG4 0.005856 0.000549 10.67451 0.0000
R-squared 0.989242 Mean dependent var 123.3300
Adjusted R-squared 0.988446 S.D. dependent var 28.79514
S.E. of regression 3.095233 Akaike info criterion 5.192243
Sum squared resid 258.6727 Schwarz criterion 5.332363
Log likelihood -74.88365 F-statistic 1241.430
Durbin-Watson stat 1.665191 Prob(F-statistic) 0.000000
80
100
120
140
160
180
200
1960 1965 1970 1975 1980 1985 1990 1995
Actual Fitted
Beşeri Sermaye ModeliBeşeri Sermaye Modeli
r= Her ilave eğitim yılının getiri oranı
Bir yıl ilave eğitimin getirisi: w1= (1+r).w0
İki yıl ilave eğitimin getirisi: w2= (1+r)2.w0
s yıl ilave eğitimin getirisi: ws= (1+r)s.w0
ln( ws) = s.ln (1+r) + ln(w0)
ln( ws) = b1 + b2.s
DATA6-4: Data on salaries and employment characteristics of 49 employees in a certain company. Data compiled by Susan Wong
WAGE = Wage rate per month (Range 981 - 3833)
EDUC = Years of education beyond 8th grade when hired (Range 1 - 11)
EXPER = Number of years at the company (Range 1 - 23)
AGE = Age of employee (25 - 64)
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
EDUC 0.064553 0.016750 3.853948 0.0004
EXPER 0.022700 0.006873 3.302822 0.0019
AGE 0.000392 0.004033 0.097144 0.9230
C 6.835956 0.203431 33.60335 0.0000
R-squared 0.327625 Mean dependent var 7.454952
Adjusted R-squared 0.282800 S.D. dependent var 0.312741
S.E. of regression 0.264853 Akaike info criterion 0.258822
Sum squared resid 3.156615 Schwarz criterion 0.413256
Log likelihood -2.341143 F-statistic 7.308992
Durbin-Watson stat 1.606966 Prob(F-statistic) 0.000429
Redundant Variables: AGE
F-statistic 0.009437 Probability 0.923043
Log likelihood ratio 0.010275 Probability 0.919261
Test Equation:
Dependent Variable: LOG(WAGE)
Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
EDUC 0.064505 0.016561 3.894924 0.0003
EXPER 0.022954 0.006285 3.652488 0.0007
C 6.850604 0.135079 50.71544 0.0000
R-squared 0.327484 Akaike info criterion 0.218216
Adjusted R-squared 0.298245 Schwarz criterion 0.334041
S.E. of regression 0.261986 F-statistic 11.19995
Sum squared resid 3.157276 Prob(F-statistic) 0.000109
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.329325 0.809178 9.057746 0.0000
EDUC -0.093041 0.086385 -1.077050 0.2876
EXPER 0.013863 0.024484 0.566210 0.5743
AGE -0.000426 0.033821 -0.012598 0.9900
EDUC^2 0.011525 0.006274 1.836991 0.0733
EXPER^2 0.000429 0.001119 0.383709 0.7031
AGE^2 2.11E-05 0.000381 0.055452 0.9560
R-squared 0.380615 Mean dependent var 7.454952
Adjusted R-squared 0.292131 S.D. dependent var 0.312741
S.E. of regression 0.263124 Akaike info criterion 0.299183
Sum squared resid 2.907844 Schwarz criterion 0.569443
Log likelihood -0.329981 F-statistic 4.301529
Durbin-Watson stat 1.836202 Prob(F-statistic) 0.001816
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.319851 0.295150 24.80047 0.0000
EDUC -0.092871 0.084324 -1.101355 0.2769
EXPER 0.013886 0.024130 0.575473 0.5680
EDUC^2 0.011511 0.006112 1.883367 0.0664
EXPER^2 0.000428 0.001098 0.389398 0.6989
AGE^2 1.64E-05 4.51E-05 0.363167 0.7183
R-squared 0.380612 Mean dependent var 7.454952
Adjusted R-squared 0.308591 S.D. dependent var 0.312741
S.E. of regression 0.260047 Akaike info criterion 0.258370
Sum squared resid 2.907855 Schwarz criterion 0.490022
Log likelihood -0.330074 F-statistic 5.284683
Durbin-Watson stat 1.836170 Prob(F-statistic) 0.000718
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.330007 0.290909 25.19693 0.0000
EDUC -0.088259 0.082536 -1.069337 0.2907
EXPER 0.014847 0.023747 0.625192 0.5351
EDUC^2 0.011154 0.005972 1.867523 0.0685
EXPER^2 0.000424 0.001087 0.390167 0.6983
R-squared 0.378713 Mean dependent var 7.454952
Adjusted R-squared 0.322232 S.D. dependent var 0.312741
S.E. of regression 0.257469 Akaike info criterion 0.220617
Sum squared resid 2.916774 Schwarz criterion 0.413659
Log likelihood -0.405106 F-statistic 6.705173
Durbin-Watson stat 1.778651 Prob(F-statistic) 0.000264
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.286796 0.266457 27.34701 0.0000
EDUC -0.085943 0.081543 -1.053958 0.2975
EXPER 0.023791 0.006134 3.878702 0.0003
EDUC^2 0.011134 0.005916 1.882161 0.0663
R-squared 0.376563 Mean dependent var 7.454952
Adjusted R-squared 0.335001 S.D. dependent var 0.312741
S.E. of regression 0.255032 Akaike info criterion 0.183254
Sum squared resid 2.926865 Schwarz criterion 0.337688
Log likelihood -0.489724 F-statistic 9.060174
Durbin-Watson stat 1.778074 Prob(F-statistic) 0.000083
Dependent Variable: LOG(WAGE) Included observations: 49
Variable Coefficient Std. Error t-Statistic Prob.
C 7.023367 0.092457 75.96326 0.0000
EXPER 0.023681 0.006140 3.856595 0.0004
EDUC^2 0.005023 0.001171 4.289093 0.0001
R-squared 0.361174 Mean dependent var 7.454952
Adjusted R-squared 0.333398 S.D. dependent var 0.312741
S.E. of regression 0.255339 Akaike info criterion 0.166823
Sum squared resid 2.999115 Schwarz criterion 0.282649
Log likelihood -1.087164 F-statistic 13.00352
Durbin-Watson stat 1.691273 Prob(F-statistic) 0.000033
DATA4-4: Demand for bus travel and its determinantsAll data are for the year 1988 for 40 cities across the U.S. Data compiled by Sean Naughton
BUSTRAVL = Demand for urban tranportation by bus in thousands of passenger hours (Range 18.1 - 1310.3)
FARE = Bus fare in dollars (Range 0.5 - 1.5)
GASPRICE = Price of a gallon of gasoline, in $ (Range 0.79 - 1.03)
INCOME = Average income PER CAPITA (Range 12349 - 21886)
POP = Population of city in thousands (Range 167 - 7323.3)
DENSITY = Density of city in persons/sq. mile (Range 1551 - 24288)
LANDAREA = Land area of the city in sq. miles (Range 18.9 - 556.4)
Dependent Variable: LOG(BUSTRAVL) Included observations: 40
Variable Coefficient Std. Error t-Statistic Prob.
C 44.71498 20.74953 2.154988 0.0386
LOG(FARE) 0.476381 0.425336 1.120010 0.2708
LOG(DENSITY) 0.275586 2.662865 0.103492 0.9182
LOG(GASPRICE) -1.732969 2.495004 -0.694576 0.4922
LOG(INCOME) -4.852523 1.047345 -4.633168 0.0001
LOG(LANDAREA) -0.816762 2.713267 -0.301025 0.7653
LOG(POP) 1.686758 2.695821 0.625694 0.5358
R-squared 0.656977 Mean dependent var 7.023257
Adjusted R-squared 0.594609 S.D. dependent var 1.157544
S.E. of regression 0.737012 Akaike info criterion 2.385203
Sum squared resid 17.92516 Schwarz criterion 2.680757
Log likelihood -40.70406 F-statistic 10.53389
Durbin-Watson stat 1.926317 Prob(F-statistic) 0.000002
Dependent Variable: LOG(BUSTRAVL) Included observations: 40
Variable Coefficient Std. Error t-Statistic Prob.
C 46.60735 9.664370 4.822596 0.0000
LOG(FARE) 0.492059 0.391617 1.256479 0.2175
LOG(GASPRICE) -1.710396 2.449026 -0.698398 0.4897
LOG(INCOME) -4.850320 1.031782 -4.700917 0.0000
LOG(LANDAREA) -1.096442 0.238906 -4.589419 0.0001
LOG(POP) 1.964220 0.278327 7.057246 0.0000
R-squared 0.656865 Mean dependent var 7.023257
Adjusted R-squared 0.606404 S.D. dependent var 1.157544
S.E. of regression 0.726211 Akaike info criterion 2.335528
Sum squared resid 17.93098 Schwarz criterion 2.588860
Log likelihood -40.71055 F-statistic 13.01729
Durbin-Watson stat 1.926467 Prob(F-statistic) 0.000000
Dependent Variable: LOG(BUSTRAVL) Included observations: 40
Variable Coefficient Std. Error t-Statistic Prob.
C 46.20138 9.576020 4.824696 0.0000
LOG(FARE) 0.438911 0.381331 1.150999 0.2575
LOG(INCOME) -4.765488 1.017081 -4.685453 0.0000
LOG(LANDAREA) -1.019002 0.210062 -4.850956 0.0000
LOG(POP) 1.865398 0.237915 7.840611 0.0000
R-squared 0.651943 Mean dependent var 7.023257
Adjusted R-squared 0.612165 S.D. dependent var 1.157544
S.E. of regression 0.720877 Akaike info criterion 2.299772
Sum squared resid 18.18822 Schwarz criterion 2.510881
Log likelihood -40.99543 F-statistic 16.38954
Durbin-Watson stat 1.971960 Prob(F-statistic) 0.000000
Omitted Variables: LOG(FARE) LOG(DENSITY) LOG(GASPRICE)
F-statistic 0.583902 Probability 0.629794
Log likelihood ratio 2.068843 Probability 0.558242
Dependent Variable: LOG(BUSTRAVL) Included observations: 40
Variable Coefficient Std. Error t-Statistic Prob.
C 45.84568 9.614110 4.768582 0.0000
LOG(INCOME) -4.730082 1.021192 -4.631923 0.0000
LOG(LANDAREA) -0.970997 0.206807 -4.695192 0.0000
LOG(POP) 1.820371 0.235733 7.722176 0.0000
R-squared 0.638768 Mean dependent var 7.023257
Adjusted R-squared 0.608666 S.D. dependent var 1.157544
S.E. of regression 0.724121 Akaike info criterion 2.286924
Sum squared resid 18.87667 Schwarz criterion 2.455812
Log likelihood -41.73848 F-statistic 21.21967
Durbin-Watson stat 2.054301 Prob(F-statistic) 0.000000