#linear regression with & with out interception #1 WITH interception table 13

library(wooldridge)
library(rmarkdown)
data("fertil1")
paged_table(fertil1)
require(dplyr)
## Zorunlu paket yükleniyor: dplyr
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
fertil1 %>%
group_by(year) %>%
summarise(mean(kids))
## # A tibble: 7 × 2
##    year `mean(kids)`
##   <int>        <dbl>
## 1    72         3.03
## 2    74         3.21
## 3    76         2.80
## 4    78         2.80
## 5    80         2.82
## 6    82         2.40
## 7    84         2.24
max(fertil1)
## [1] 2916
fertil1 %>%
group_by(year) %>%
summarise(mean(kids), sd(kids))
## # A tibble: 7 × 3
##    year `mean(kids)` `sd(kids)`
##   <int>        <dbl>      <dbl>
## 1    72         3.03       1.83
## 2    74         3.21       1.50
## 3    76         2.80       1.66
## 4    78         2.80       1.58
## 5    80         2.82       1.58
## 6    82         2.40       1.70
## 7    84         2.24       1.51
fertil1 %>%
group_by(year) %>%
summarise(across(everything(),mean))
## # A tibble: 7 × 27
##    year  educ meduc feduc   age  kids  black  east northcen   west  farm othru…¹
##   <int> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl>    <dbl>  <dbl> <dbl>   <dbl>
## 1    72  12.2  8.33  8.90  44.9  3.03 0.0833 0.333    0.231 0.128  0.173  0.0833
## 2    74  12.3  8.94  9.29  44.1  3.21 0.0578 0.237    0.353 0.110  0.208  0.110 
## 3    76  12.2  8.25  8.99  43.5  2.80 0.0461 0.263    0.316 0.0855 0.237  0.112 
## 4    78  12.6  9.07  9.80  43.4  2.80 0.0490 0.273    0.329 0.105  0.203  0.112 
## 5    80  12.9  9.40  9.95  43.7  2.82 0.0704 0.141    0.394 0.155  0.218  0.106 
## 6    82  13.2  9.56 10.2   43.2  2.40 0.199  0.231    0.290 0.0806 0.167  0.118 
## 7    84  13.3 10.2  10.7   41.8  2.24 0.0678 0.260    0.333 0.102  0.192  0.0734
## # … with 15 more variables: town <dbl>, smcity <dbl>, y74 <dbl>, y76 <dbl>,
## #   y78 <dbl>, y80 <dbl>, y82 <dbl>, y84 <dbl>, agesq <dbl>, y74educ <dbl>,
## #   y76educ <dbl>, y78educ <dbl>, y80educ <dbl>, y82educ <dbl>, y84educ <dbl>,
## #   and abbreviated variable name ¹​othrural
summary(lm(formula = kids ~ educ + age + kids + black + east + west + farm + othrural + town + smcity + northcen + y74 + y76 + y78 + y80 + y82 + y84, data = fertil1))
## Warning in model.matrix.default(mt, mf, contrasts): the response appeared on the
## right-hand side and was dropped
## Warning in model.matrix.default(mt, mf, contrasts): problem with term 3 in
## model.matrix: no columns are assigned
## 
## Call:
## lm(formula = kids ~ educ + age + kids + black + east + west + 
##     farm + othrural + town + smcity + northcen + y74 + y76 + 
##     y78 + y80 + y82 + y84, data = fertil1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.3513 -1.0528 -0.0532  1.0103  4.7589 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  3.445625   0.472469   7.293 5.75e-13 ***
## educ        -0.131316   0.018437  -7.122 1.90e-12 ***
## age          0.019556   0.008143   2.402 0.016488 *  
## black        1.051224   0.174403   6.028 2.26e-09 ***
## east         0.220476   0.133545   1.651 0.099031 .  
## west         0.170869   0.167712   1.019 0.308509    
## farm        -0.053842   0.148032  -0.364 0.716138    
## othrural    -0.160079   0.176445  -0.907 0.364471    
## town         0.088927   0.125238   0.710 0.477810    
## smcity       0.227803   0.161156   1.414 0.157771    
## northcen     0.350287   0.121539   2.882 0.004026 ** 
## y74          0.239607   0.173532   1.381 0.167629    
## y76         -0.141232   0.179678  -0.786 0.432018    
## y78         -0.107941   0.182413  -0.592 0.554146    
## y80         -0.090874   0.183740  -0.495 0.620995    
## y82         -0.553466   0.173220  -3.195 0.001437 ** 
## y84         -0.589178   0.175109  -3.365 0.000793 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.564 on 1112 degrees of freedom
## Multiple R-squared:  0.1187, Adjusted R-squared:  0.106 
## F-statistic: 9.363 on 16 and 1112 DF,  p-value: < 2.2e-16
fertil1 %>%
group_by(year) %>%
plot(fertil1)

#2 linear regression WITHOUT intercept

#we can do linear regression without intercept in 3 different way

way 1

summary(lm(formula = kids ~ 0 + educ + age + kids + black + east + west + farm + othrural + town + smcity + northcen + y74 + y76 + y78 + y80 + y82 + y84, data = fertil1))
## Warning in model.matrix.default(mt, mf, contrasts): the response appeared on the
## right-hand side and was dropped
## Warning in model.matrix.default(mt, mf, contrasts): problem with term 3 in
## model.matrix: no columns are assigned
## 
## Call:
## lm(formula = kids ~ 0 + educ + age + kids + black + east + west + 
##     farm + othrural + town + smcity + northcen + y74 + y76 + 
##     y78 + y80 + y82 + y84, data = fertil1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9406 -1.0116 -0.0284  1.0615  4.8716 
## 
## Coefficients:
##           Estimate Std. Error t value Pr(>|t|)    
## educ     -0.059614   0.015958  -3.736 0.000197 ***
## age       0.067067   0.004998  13.417  < 2e-16 ***
## black     1.159675   0.177795   6.523 1.05e-10 ***
## east      0.349080   0.135444   2.577 0.010085 *  
## west      0.306814   0.170536   1.799 0.072270 .  
## farm      0.128938   0.149276   0.864 0.387907    
## othrural  0.087305   0.177166   0.493 0.622261    
## town      0.217314   0.126868   1.713 0.087006 .  
## smcity    0.352197   0.163964   2.148 0.031928 *  
## northcen  0.438681   0.123736   3.545 0.000408 ***
## y74       0.508975   0.173485   2.934 0.003417 ** 
## y76       0.153246   0.179139   0.855 0.392483    
## y78       0.161320   0.182778   0.883 0.377641    
## y80       0.151723   0.184892   0.821 0.412048    
## y82      -0.309474   0.173897  -1.780 0.075407 .  
## y84      -0.279759   0.173829  -1.609 0.107814    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.6 on 1113 degrees of freedom
## Multiple R-squared:  0.754,  Adjusted R-squared:  0.7504 
## F-statistic: 213.2 on 16 and 1113 DF,  p-value: < 2.2e-16

#way 2

summary(lm(formula = kids ~ educ + age + kids + black + east + west + farm + othrural + town + smcity + northcen + y74 + y76 + y78 + y80 + y82 + y84 -1, data = fertil1))
## Warning in model.matrix.default(mt, mf, contrasts): the response appeared on the
## right-hand side and was dropped
## Warning in model.matrix.default(mt, mf, contrasts): problem with term 3 in
## model.matrix: no columns are assigned
## 
## Call:
## lm(formula = kids ~ educ + age + kids + black + east + west + 
##     farm + othrural + town + smcity + northcen + y74 + y76 + 
##     y78 + y80 + y82 + y84 - 1, data = fertil1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9406 -1.0116 -0.0284  1.0615  4.8716 
## 
## Coefficients:
##           Estimate Std. Error t value Pr(>|t|)    
## educ     -0.059614   0.015958  -3.736 0.000197 ***
## age       0.067067   0.004998  13.417  < 2e-16 ***
## black     1.159675   0.177795   6.523 1.05e-10 ***
## east      0.349080   0.135444   2.577 0.010085 *  
## west      0.306814   0.170536   1.799 0.072270 .  
## farm      0.128938   0.149276   0.864 0.387907    
## othrural  0.087305   0.177166   0.493 0.622261    
## town      0.217314   0.126868   1.713 0.087006 .  
## smcity    0.352197   0.163964   2.148 0.031928 *  
## northcen  0.438681   0.123736   3.545 0.000408 ***
## y74       0.508975   0.173485   2.934 0.003417 ** 
## y76       0.153246   0.179139   0.855 0.392483    
## y78       0.161320   0.182778   0.883 0.377641    
## y80       0.151723   0.184892   0.821 0.412048    
## y82      -0.309474   0.173897  -1.780 0.075407 .  
## y84      -0.279759   0.173829  -1.609 0.107814    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.6 on 1113 degrees of freedom
## Multiple R-squared:  0.754,  Adjusted R-squared:  0.7504 
## F-statistic: 213.2 on 16 and 1113 DF,  p-value: < 2.2e-16

way3

summary(lm(formula = kids ~ educ + age + kids + black + east + west + farm + othrural + town + smcity + northcen + y74 + y76 + y78 + y80 + y82 + y84 + 0, data = fertil1))
## Warning in model.matrix.default(mt, mf, contrasts): the response appeared on the
## right-hand side and was dropped
## Warning in model.matrix.default(mt, mf, contrasts): problem with term 3 in
## model.matrix: no columns are assigned
## 
## Call:
## lm(formula = kids ~ educ + age + kids + black + east + west + 
##     farm + othrural + town + smcity + northcen + y74 + y76 + 
##     y78 + y80 + y82 + y84 + 0, data = fertil1)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.9406 -1.0116 -0.0284  1.0615  4.8716 
## 
## Coefficients:
##           Estimate Std. Error t value Pr(>|t|)    
## educ     -0.059614   0.015958  -3.736 0.000197 ***
## age       0.067067   0.004998  13.417  < 2e-16 ***
## black     1.159675   0.177795   6.523 1.05e-10 ***
## east      0.349080   0.135444   2.577 0.010085 *  
## west      0.306814   0.170536   1.799 0.072270 .  
## farm      0.128938   0.149276   0.864 0.387907    
## othrural  0.087305   0.177166   0.493 0.622261    
## town      0.217314   0.126868   1.713 0.087006 .  
## smcity    0.352197   0.163964   2.148 0.031928 *  
## northcen  0.438681   0.123736   3.545 0.000408 ***
## y74       0.508975   0.173485   2.934 0.003417 ** 
## y76       0.153246   0.179139   0.855 0.392483    
## y78       0.161320   0.182778   0.883 0.377641    
## y80       0.151723   0.184892   0.821 0.412048    
## y82      -0.309474   0.173897  -1.780 0.075407 .  
## y84      -0.279759   0.173829  -1.609 0.107814    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.6 on 1113 degrees of freedom
## Multiple R-squared:  0.754,  Adjusted R-squared:  0.7504 
## F-statistic: 213.2 on 16 and 1113 DF,  p-value: < 2.2e-16