Interpreting the coefficients of multiple LRM

Purpose of this post is to explain Frisch-Waught in a very simple form as many a times students in econometric classes are used to memorize the concept \(y=\beta_0x+\beta_1x_1+\beta_2x_2+\epsilon\) Using the data set Growth described (description is provided in previous video), excluding the data for Malta, run the following five regressions: Growth on
(1) TradeShare and YearsSchool;

library(readxl)
library(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
library(moderndive)
library(gridExtra)
## Warning: package 'gridExtra' was built under R version 3.6.2
## 
## Attaching package: 'gridExtra'
## The following object is masked from 'package:dplyr':
## 
##     combine
library(ggplot2)
library(stargazer)
## 
## Please cite as:
##  Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.2. https://CRAN.R-project.org/package=stargazer
Growth <- read_excel("C:/Users/hp/Dropbox/Applied Economics/Growth.xlsx")

glimpse(Growth)
## Observations: 65
## Variables: 7
## $ country_name  <chr> "India", "Argentina", "Japan", "Brazil", "United Stat...
## $ growth        <dbl> 1.9151680, 0.6176451, 4.3047590, 2.9300970, 1.7122650...
## $ rgdp60        <dbl> 765.9998, 4462.0010, 2954.0000, 1784.0000, 9895.0040,...
## $ tradeshare    <dbl> 0.1405020, 0.1566230, 0.1577032, 0.1604051, 0.1608150...
## $ yearsschool   <dbl> 1.45, 4.99, 6.71, 2.89, 8.66, 0.79, 3.80, 2.97, 3.02,...
## $ rev_coups     <dbl> 0.1333333, 0.9333333, 0.0000000, 0.1000000, 0.0000000...
## $ assasinations <dbl> 0.8666667, 1.9333330, 0.2000000, 0.1000000, 0.4333333...
growth_malta<-Growth %>% filter(country_name!="Malta")

mod.lm1<-lm(growth~tradeshare+yearsschool,data = growth_malta)
mod.lm2<-lm(growth~yearsschool,data = growth_malta)
mod.lm3<-lm(tradeshare~yearsschool,data = growth_malta)
gr_yrs<-mod.lm2$residuals
trsh_yrs<-mod.lm3$residuals
mod.lm4<-lm(gr_yrs~trsh_yrs)
get_regression_table(mod.lm1)
## # A tibble: 3 x 7
##   term        estimate std_error statistic p_value lower_ci upper_ci
##   <chr>          <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
## 1 intercept     -0.122     0.663    -0.184   0.854   -1.45      1.20
## 2 tradeshare     1.90      0.936     2.03    0.047    0.026     3.77
## 3 yearsschool    0.243     0.084     2.90    0.005    0.076     0.41
get_regression_table(mod.lm4)
## # A tibble: 2 x 7
##   term      estimate std_error statistic p_value lower_ci upper_ci
##   <chr>        <dbl>     <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
## 1 intercept     0        0.21       0      1       -0.419    0.419
## 2 trsh_yrs      1.90     0.928      2.04   0.045    0.042    3.75
stargazer(mod.lm1,mod.lm4,type = "text")
## 
## ==============================================================
##                                Dependent variable:            
##                     ------------------------------------------
##                            growth                gr_yrs       
##                              (1)                  (2)         
## --------------------------------------------------------------
## tradeshare                 1.898**                            
##                            (0.936)                            
##                                                               
## yearsschool               0.243***                            
##                            (0.084)                            
##                                                               
## trsh_yrs                                        1.898**       
##                                                 (0.928)       
##                                                               
## Constant                   -0.122                0.000        
##                            (0.663)              (0.210)       
##                                                               
## --------------------------------------------------------------
## Observations                 64                    64         
## R2                          0.161                0.063        
## Adjusted R2                 0.133                0.048        
## Residual Std. Error    1.691 (df = 61)      1.677 (df = 62)   
## F Statistic         5.836*** (df = 2; 61) 4.178** (df = 1; 62)
## ==============================================================
## Note:                              *p<0.1; **p<0.05; ***p<0.01