library(wooldridge)
data("kielmc")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)
\(log(price)=β0+β1log(dist)+u\)
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-10Evin 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 10.73640reg2 <- 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(iii) (ii). şıktaki modele [log(intst)]^2 ekleyiniz.Şimdi ne olur? Modelin fonksiyonel şeklinin önemi hakkında nasıl bir sonuca ulaşırsınız?
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(iv) log(dist)'in karesi (iii).şıktaki modele eklendiğinde anlamlı mıdır?
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