library(wooldridge)
## Warning: le package 'wooldridge' a été compilé avec la version R 4.2.2
data(kielmc)
help("kielmc")
## démarrage du serveur d'aide httpd ... fini

Format A data.frame with 321 observations on 25 variables:

year: 1978 or 1981

age: age of house

agesq: age^2

nbh: neighborhood, 1-6

cbd: dist. to cent. bus. dstrct, ft.

intst: dist. to interstate, ft.

lintst: log(intst)

price: selling price

rooms: # rooms in house

area: square footage of house

land: square footage lot

baths: # bathrooms

dist: dist. from house to incin., ft.

ldist: log(dist)

wind: prc. time wind incin. to house

lprice: log(price)

y81: =1 if year == 1981

larea: log(area)

lland: log(land)

y81ldist: y81*ldist

lintstsq: lintst^2

nearinc: =1 if dist <= 15840

y81nrinc: y81*nearinc

rprice: price, 1978 dollars

lrprice: log(rprice)

B6.1.Sadece 1981 yılı için,KIELMC.RAW’daki verileri kullanarak aşağıdaki sorulara cevap veriniz.Veriler 1981’de Kuzey Andover,Massachuaetts’te satılan evlerdir.1981,yerel çöp yakma fırınının kurulmaya başlandığı yıldı. (i) Çöp yakma fırının konumunun ev fiyatları üzerindeki etkisini incelemek için şu basit modeli ele alalım:

\[log(price)=β0+β1log(dist)+u\]

Burada price dolar cinsinden evin fiyatı ve dist,ev ile çöp yakma fırını arasındaki adım cinsinden uzaklıktır.Denklemin dikkatli biçimde yorumlanmasında çöp yakma fırınının bulunması ev fiyatlarını düşürüyorsa β1 ’in işaretini ne beklersiniz? Cevap β1 pozitiftir.

reg1 <- lm(log(price) ~ log(dist) , data = kielmc)
summary(reg1)
## 
## Call:
## lm(formula = log(price) ~ log(dist), data = kielmc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.22356 -0.28076 -0.05527  0.27992  1.29332 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  8.25750    0.47383  17.427  < 2e-16 ***
## log(dist)    0.31722    0.04811   6.594 1.78e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4117 on 319 degrees of freedom
## Multiple R-squared:  0.1199, Adjusted R-squared:  0.1172 
## F-statistic: 43.48 on 1 and 319 DF,  p-value: 1.779e-10

(ii):(i) şıkkındaki basit regresyon modeline,log(intst),log(area),log(land),oda sayısı(rooms),banyo sayısı(baths) ve yaş(age) değişkenini ekleyelim.şimdi çöp yakma fırınının etkileri hakkında nasıl bir sonuca ulaşırsınız? Cevap Evin diğer özelliklerini ekleyince çöp yakma fırınının fiyata etkisi azalmıştır.

head(kielmc)
##   year age agesq nbh  cbd intst lintst price rooms area  land baths  dist
## 1 1978  48  2304   4 3000  1000 6.9078 60000     7 1660  4578     1 10700
## 2 1978  83  6889   4 4000  1000 6.9078 40000     6 2612  8370     2 11000
## 3 1978  58  3364   4 4000  1000 6.9078 34000     6 1144  5000     1 11500
## 4 1978  11   121   4 4000  1000 6.9078 63900     5 1136 10000     1 11900
## 5 1978  48  2304   4 4000  2000 7.6009 44000     5 1868 10000     1 12100
## 6 1978  78  6084   4 3000  2000 7.6009 46000     6 1780  9500     3 10000
##      ldist wind   lprice y81    larea    lland y81ldist lintstsq nearinc
## 1 9.277999    3 11.00210   0 7.414573 8.429017        0 47.71770       1
## 2 9.305651    3 10.59663   0 7.867871 9.032409        0 47.71770       1
## 3 9.350102    3 10.43412   0 7.042286 8.517193        0 47.71770       1
## 4 9.384294    3 11.06507   0 7.035269 9.210340        0 47.71770       1
## 5 9.400961    3 10.69195   0 7.532624 9.210340        0 57.77368       1
## 6 9.210340    3 10.73640   0 7.484369 9.159047        0 57.77368       1
##   y81nrinc rprice  lrprice
## 1        0  60000 11.00210
## 2        0  40000 10.59663
## 3        0  34000 10.43412
## 4        0  63900 11.06507
## 5        0  44000 10.69195
## 6        0  46000 10.73640
reg2 <- lm(log(price) ~ log(dist)+log(intst)+log(area)+log(land)+rooms+baths+age ,data = kielmc)
summary(reg2)
## 
## Call:
## lm(formula = log(price) ~ log(dist) + log(intst) + log(area) + 
##     log(land) + rooms + baths + age, data = kielmc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.35838 -0.18220  0.00115  0.20532  0.82180 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  6.2996586  0.5960546  10.569  < 2e-16 ***
## log(dist)    0.0281887  0.0532130   0.530  0.59667    
## log(intst)  -0.0437804  0.0424359  -1.032  0.30302    
## log(area)    0.5124071  0.0698229   7.339 1.87e-12 ***
## log(land)    0.0782098  0.0337206   2.319  0.02102 *  
## rooms        0.0503129  0.0235113   2.140  0.03313 *  
## baths        0.1070528  0.0352304   3.039  0.00258 ** 
## age         -0.0035630  0.0005774  -6.171 2.10e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2828 on 313 degrees of freedom
## Multiple R-squared:  0.5925, Adjusted R-squared:  0.5834 
## F-statistic: 65.02 on 7 and 313 DF,  p-value: < 2.2e-16
  1. (ii). şıktaki modele [log(intst)]^2 ekleyiniz.Şimdi ne olur? Modelin fonksiyonel şeklinin önemi hakkında nasıl bir sonuca ulaşırsınız? Cevap Ev otoyoldan uzaklaştıkça evin fiyatı azalır.
reg3 <- lm(log(price) ~ log(dist)+log(intst)+log(area)+log(land)+rooms+baths+age+lintstsq , data = kielmc)
summary(reg3)
## 
## Call:
## lm(formula = log(price) ~ log(dist) + log(intst) + log(area) + 
##     log(land) + rooms + baths + age + lintstsq, data = kielmc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.41726 -0.17786  0.01087  0.19286  0.72075 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -3.7940563  2.2944105  -1.654  0.09921 .  
## log(dist)    0.1898078  0.0626753   3.028  0.00266 ** 
## log(intst)   1.9031553  0.4302516   4.423 1.34e-05 ***
## log(area)    0.5136595  0.0677282   7.584 3.87e-13 ***
## log(land)    0.1069039  0.0333122   3.209  0.00147 ** 
## rooms        0.0495164  0.0228064   2.171  0.03067 *  
## baths        0.0899004  0.0343809   2.615  0.00936 ** 
## age         -0.0035709  0.0005601  -6.376 6.55e-10 ***
## lintstsq    -0.1128807  0.0248310  -4.546 7.83e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2743 on 312 degrees of freedom
## Multiple R-squared:  0.6178, Adjusted R-squared:  0.608 
## F-statistic: 63.05 on 8 and 312 DF,  p-value: < 2.2e-16
  1. log(dist)’in karesi (iii).şıktaki modele eklendiğinde anlamlı mıdır? Cevap log(dist)’in karesini modele eklediğimizde sonuç anlamlı olur.
reg4 <- lm(log(price) ~ log(dist)+log(intst)+log(area)+log(land)+rooms+baths+age+I(log(dist)^2) ,data = kielmc)
summary(reg4)
## 
## Call:
## lm(formula = log(price) ~ log(dist) + log(intst) + log(area) + 
##     log(land) + rooms + baths + age + I(log(dist)^2), data = kielmc)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.40274 -0.18638 -0.01379  0.19742  0.75931 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -1.833e+01  6.537e+00  -2.804 0.005361 ** 
## log(dist)       5.120e+00  1.347e+00   3.801 0.000173 ***
## log(intst)      3.747e-02  4.678e-02   0.801 0.423765    
## log(area)       4.936e-01  6.856e-02   7.199 4.55e-12 ***
## log(land)       6.819e-02  3.313e-02   2.058 0.040404 *  
## rooms           4.536e-02  2.306e-02   1.967 0.050088 .  
## baths           9.626e-02  3.462e-02   2.780 0.005758 ** 
## age            -3.445e-03  5.664e-04  -6.083 3.45e-09 ***
## I(log(dist)^2) -2.673e-01  7.065e-02  -3.783 0.000186 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.277 on 312 degrees of freedom
## Multiple R-squared:  0.6104, Adjusted R-squared:  0.6004 
## F-statistic:  61.1 on 8 and 312 DF,  p-value: < 2.2e-16