data set: Journals

資料整理

journals <- Journals %>%
  mutate(
    citeprice = price/citations, 
    age = 2000-foundingyear, 
    chars = charpp * pages / 10^6
  )

journals %>% rmarkdown::paged_table()

\[ citeprice = \frac{price}{citations} \]

\[ age = 2000 - foundingyear \]

其中2000年為統計這個資料集時的年度

\[ chars = charpp \times pages \]

journals %>%
  select(subs, citeprice) %>% 
  pairs.panels()

journals %>%
  select(subs, citeprice) %>%
  mutate_all(log) %>%
  pairs.panels()

journals1 <- journals %>%
  select(subs, citeprice, age, chars) %>%
  mutate_all(log)

\[ subs = \beta_0+\beta_1 citeprice + \beta_2 age + \beta_3 chars +\varepsilon_i \]

model1 <- journals1 %>%
  lm(formula = subs ~ citeprice + age + chars, data = .)
coeftest(model1, vcov. = vcovHC, type = "HC1")

t test of coefficients:

             Estimate Std. Error t value  Pr(>|t|)    
(Intercept)  3.206648   0.379725  8.4447 1.102e-14 ***
citeprice   -0.407718   0.043717 -9.3262 < 2.2e-16 ***
age          0.423649   0.119064  3.5581 0.0004801 ***
chars        0.205614   0.097751  2.1035 0.0368474 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[ \begin{aligned} subs =& \beta_0+\beta_1 citeprice + \beta_2 citeprice^2 +\beta_3 citeprice^3 \\&+ \beta_4 citeprice * age+\beta_4 age + \beta_5 chars + \varepsilon_i \end{aligned} \]

model2 <- journals1 %>%
  lm(formula = subs ~ citeprice + I(citeprice^2) + I(citeprice^3) + I(age * citeprice)+ age + chars, data = .)
coeftest(model2, vcov. = vcovHC, type = "HC1")

t test of coefficients:

                     Estimate Std. Error t value  Pr(>|t|)    
(Intercept)         3.4075956  0.3735992  9.1210 < 2.2e-16 ***
citeprice          -0.9609365  0.1601349 -6.0008 1.121e-08 ***
I(citeprice^2)      0.0165099  0.0254886  0.6477  0.518015    
I(citeprice^3)      0.0036666  0.0055147  0.6649  0.507008    
I(age * citeprice)  0.1557773  0.0518947  3.0018  0.003081 ** 
age                 0.3730539  0.1176966  3.1696  0.001805 ** 
chars               0.2346178  0.0977318  2.4006  0.017428 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

\[ \begin{aligned} subs = \beta_0+\beta_1 citeprice + \beta_2 age + \beta_3 age* citeprice + \beta_4 chars + \varepsilon_i \end{aligned} \]

model3 <- journals1 %>%
  lm(formula = subs ~ citeprice + age + I(age * citeprice) + chars, data = .)

coeftest(model3, vcov. = vcovHC, type = "HC1")

t test of coefficients:

                    Estimate Std. Error t value  Pr(>|t|)    
(Intercept)         3.433521   0.367471  9.3436 < 2.2e-16 ***
citeprice          -0.898910   0.144648 -6.2144 3.656e-09 ***
age                 0.373515   0.117527  3.1781 0.0017529 ** 
I(age * citeprice)  0.140959   0.040199  3.5065 0.0005769 ***
chars               0.229466   0.096493  2.3781 0.0184822 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1