##soru(i):Çöp 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 B1işaretini ne beklerseniz? Denklemi tahmin edin ve sonuçları yorumlayınız. ##cevap: B1 işaretini negatiftir
library(wooldridge)data("kielmc",package = 'wooldridge') head(kielmc,20)## 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
## 7 1978 22 484 4 4000 2000 7.6009 56000 6 1700 10878 2 11700
## 8 1978 78 6084 4 3000 2000 7.6009 38500 6 1556 3870 2 10200
## 9 1978 42 1764 4 3000 2000 7.6009 60500 8 1642 7000 2 10500
## 10 1978 41 1681 4 3000 2000 7.6009 55000 5 1443 7950 2 11000
## 11 1978 78 6084 4 1000 4000 8.2940 39000 6 1439 4990 1 8600
## 12 1978 38 1444 0 6000 4000 8.2940 41000 5 1482 8017 1 12200
## 13 1978 18 324 0 5000 4000 8.2940 50900 6 1290 12538 2 12400
## 14 1978 32 1024 0 9000 7000 8.8537 52000 6 1274 7858 1 16800
## 15 1978 18 324 0 9000 8000 8.9872 49000 6 1476 15664 1 17200
## 16 1978 58 3364 4 2000 3000 8.0064 80000 7 1838 9249 2 9900
## 17 1978 56 3136 4 2000 3000 8.0064 50000 6 1536 10491 2 10000
## 18 1978 70 4900 4 2000 3000 8.0064 59000 5 2458 9400 2 10000
## 19 1978 26 676 4 3000 4000 8.2940 42000 4 750 8000 1 10600
## 20 1978 21 441 4 4000 4000 8.2940 71500 5 2106 13370 2 11700
## 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
## 7 9.367344 3 10.93311 0 7.438384 9.294497 0 57.77368 1
## 8 9.230143 3 10.55841 0 7.349874 8.261010 0 57.77368 1
## 9 9.259131 3 11.01040 0 7.403670 8.853665 0 57.77368 1
## 10 9.305651 3 10.91509 0 7.274479 8.980927 0 57.77368 1
## 11 9.059517 3 10.57132 0 7.271704 8.515191 0 68.79043 1
## 12 9.409191 3 10.62133 0 7.301148 8.989320 0 68.79043 1
## 13 9.425452 3 10.83762 0 7.162397 9.436520 0 68.79043 1
## 14 9.729134 3 10.85900 0 7.149917 8.969288 0 78.38800 0
## 15 9.752665 3 10.79958 0 7.297091 9.659121 0 80.76976 0
## 16 9.200290 3 11.28978 0 7.516433 9.132271 0 64.10244 1
## 17 9.210340 3 10.81978 0 7.336937 9.258273 0 64.10244 1
## 18 9.210340 3 10.98529 0 7.807103 9.148465 0 64.10244 1
## 19 9.268609 3 10.64542 0 6.620073 8.987197 0 68.79043 1
## 20 9.367344 3 11.17745 0 7.652546 9.500769 0 68.79043 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
## 7 0 56000 10.93311
## 8 0 38500 10.55841
## 9 0 60500 11.01040
## 10 0 55000 10.91509
## 11 0 39000 10.57132
## 12 0 41000 10.62133
## 13 0 50900 10.83762
## 14 0 52000 10.85900
## 15 0 49000 10.79958
## 16 0 80000 11.28978
## 17 0 50000 10.81978
## 18 0 59000 10.98529
## 19 0 42000 10.64542
## 20 0 71500 11.17745reg<-lm (log(price)~log(dist) ,data = kielmc )
summary(reg)##
## 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##Bu basit regrasyonda diğer değişkenler farklı ve sabit tutuldu.
##soru(ii):(i)şıkkındaki basit regresyon modeline log(intst) ,log(area),log(land),oda sayısı (rooms),banyo sayısı (baths) ve yaş (age)değişkenin ekliyim.Burada intst ,ev ile otoyol arasındaki uzaklık; area, evin adım karesi; land, evin kurulu olduğu alanın adım Karesi, rooms,oda sayısı; ages, evin yıl cinsinden yaşıdır. Şimdi çöp yakma fırınının etkileri hakkında nasıl bir sonuca ulaşırsınız? (i)ve(ii) neden birbiriyle çelişkili sonuçlar verir açıklayınız.
##cevap:
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-16reg3<-lm (log(price)~log(dist)+log(intst)+log(area)+log(land)+rooms+baths+age+(log(intst))^2,data = kielmc)
summary(reg3)##
## Call:
## lm(formula = log(price) ~ log(dist) + log(intst) + log(area) +
## log(land) + rooms + baths + age + (log(intst))^2, 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-16soru(iv):log(dist),in karesi (iii)şıktakı modele eklendiğin anlamlı nedir?
##cevap:
reg4<-lm (log(price)~log(dist)+log(intst)+log(area)+log(land)+rooms+baths+age+(log(intst))^2+(log(dist))^2,data = kielmc)
summary(reg4)##
## Call:
## lm(formula = log(price) ~ log(dist) + log(intst) + log(area) +
## log(land) + rooms + baths + age + (log(intst))^2 + (log(dist))^2,
## 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