1. DATA
library(dplyr)
## Warning: package 'dplyr' was built under R version 3.6.2
## 
## 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
setwd("C:/Users/ramin/Desktop/2020 winter/Data Analysis/Computer Assignment 5/Dataset")

load(file = "OPM94.RData")
  1. CREATING NEW VARIABLE
opm94$edyrs_months = opm94$edyrs/12
  1. CORRELATION MATRIX
opm94 %>% select(sal, grade, edyrs, edyrs_months, yos, age, male01, minority) %>% 
  cor(use = "pairwise.complete.obs") %>% 
  round(2)
##                sal grade edyrs edyrs_months   yos   age male01 minority
## sal           1.00  0.91  0.59         0.59  0.40  0.29   0.36    -0.23
## grade         0.91  1.00  0.61         0.61  0.31  0.19   0.35    -0.23
## edyrs         0.59  0.61  1.00         1.00  0.01  0.08   0.31    -0.15
## edyrs_months  0.59  0.61  1.00         1.00  0.01  0.08   0.31    -0.15
## yos           0.40  0.31  0.01         0.01  1.00  0.62   0.08    -0.13
## age           0.29  0.19  0.08         0.08  0.62  1.00   0.09    -0.15
## male01        0.36  0.35  0.31         0.31  0.08  0.09   1.00    -0.12
## minority     -0.23 -0.23 -0.15        -0.15 -0.13 -0.15  -0.12     1.00
  1. REGRESSION WITH NUMERIC EXPLANATORY VARIABLES
lm(sal ~ grade, data = opm94) %>% summary()
## 
## Call:
## lm(formula = sal ~ grade, data = opm94)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -12775  -4778   -505   3413  45197 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -5132.8      698.5  -7.348 4.19e-13 ***
## grade         4779.0       68.6  69.662  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7292 on 993 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.8301, Adjusted R-squared:   0.83 
## F-statistic:  4853 on 1 and 993 DF,  p-value: < 2.2e-16
lm(grade ~ yos, data = opm94) %>% summary()
## 
## Call:
## lm(formula = grade ~ yos, data = opm94)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -8.252 -2.833  0.527  2.684  6.539 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  7.87967    0.19747   39.90   <2e-16 ***
## yos          0.11629    0.01144   10.17   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.21 on 998 degrees of freedom
## Multiple R-squared:  0.09387,    Adjusted R-squared:  0.09296 
## F-statistic: 103.4 on 1 and 998 DF,  p-value: < 2.2e-16
lm(grade ~ edyrs, data = opm94) %>% summary()
## 
## Call:
## lm(formula = grade ~ edyrs, data = opm94)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.0775 -2.0775 -0.0775  1.9225  7.5345 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -3.37071    0.54503  -6.184 9.08e-10 ***
## edyrs        0.90301    0.03748  24.095  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.681 on 998 degrees of freedom
## Multiple R-squared:  0.3678, Adjusted R-squared:  0.3671 
## F-statistic: 580.6 on 1 and 998 DF,  p-value: < 2.2e-16
lm(yos ~ age, data = opm94) %>% summary()
## 
## Call:
## lm(formula = yos ~ age, data = opm94)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -22.2467  -4.3889   0.2288   4.9875  16.6804 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -8.85485    0.96979  -9.131   <2e-16 ***
## age          0.53883    0.02151  25.056   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.96 on 998 degrees of freedom
## Multiple R-squared:  0.3861, Adjusted R-squared:  0.3855 
## F-statistic: 627.8 on 1 and 998 DF,  p-value: < 2.2e-16

Questions

4a. For each regression, briefly explain the meaning of the y-intercept and the regression coefficient.

For each regression, the y-intercept means what the dependent variable is when the independent variable equals zero.

4b. Find the expected salary for someone in 16th grade

(16*4779)-5132.8 = 71331.2

4c. Find the expected grade for someone with 5 years of service

(.11629*5)+7.87967 = 8.46112

4d. Find the expected grade for someone with 12 years of education

(.90301*12)-3.37071 = 7.46541
lm(grade ~ edyrs_months, data = opm94) %>% summary()
## 
## Call:
## lm(formula = grade ~ edyrs_months, data = opm94)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.0775 -2.0775 -0.0775  1.9225  7.5345 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   -3.3707     0.5450  -6.184 9.08e-10 ***
## edyrs_months  10.8362     0.4497  24.095  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.681 on 998 degrees of freedom
## Multiple R-squared:  0.3678, Adjusted R-squared:  0.3671 
## F-statistic: 580.6 on 1 and 998 DF,  p-value: < 2.2e-16

4e. Why is the regressin coeficient different from the coefficient on edyrs? How are they the same?

They are different because edyrs is in years and the edyrs_months is measured ed year in months. They are still the same variable in different units.
  1. REGRESSION WITH DUMMY EXPLANATORY VARIABLES
opm94 <- opm94 %>% mutate(nonvet = if_else(vet == 0, 1, 0 ))

lm(sal ~ vet, data = opm94) %>% summary()
## 
## Call:
## lm(formula = sal ~ vet, data = opm94)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -30056 -14230  -3155  10464  72731 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  39439.7      636.2  61.995  < 2e-16 ***
## vetyes        5669.8     1306.3   4.341 1.57e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17530 on 993 degrees of freedom
##   (5 observations deleted due to missingness)
## Multiple R-squared:  0.01862,    Adjusted R-squared:  0.01763 
## F-statistic: 18.84 on 1 and 993 DF,  p-value: 1.567e-05
lm(sal ~ nonvet, data = opm94) %>% summary()
## 
## Call:
## lm(formula = sal ~ nonvet, data = opm94)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -25730 -14959  -2655  10828  75745 
## 
## Coefficients: (1 not defined because of singularities)
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  40784.5      560.6   72.75   <2e-16 ***
## nonvet            NA         NA      NA       NA    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 17680 on 994 degrees of freedom
##   (5 observations deleted due to missingness)
opm94 %>% group_by(vet) %>% summarise(Mean_Salary = mean(sal, na.rm = TRUE))
## # A tibble: 2 x 2
##   vet   Mean_Salary
##   <fct>       <dbl>
## 1 no         39440.
## 2 yes        45110.
opm94 %>% group_by(nonvet) %>% summarise(Mean_Salary = mean(sal, na.rm = TRUE))
## # A tibble: 1 x 2
##   nonvet Mean_Salary
##    <dbl>       <dbl>
## 1      0      40784.

QUESTIONS

5a. Find the mean grades of veterans and nonveterans from the two rgression outputs

opm94 %>% group_by(vet) %>% summarise(Mean_grade = mean(grade, na.rm = TRUE))

opm94 %>% group_by(nonvet) %>% summarise(Mean_grade = mean(grade, na.rm = TRUE))

5b. Interpret the Y-intercepts. Why do they differ?

The y-intercept shows what salary a vet or nonvet gets at year 0. They differ, because the vets salary is less.

5c. Interpret the regression coefficients. Why do they differ?

Since there is a formula for the regression line, and there is a strong, positive relationship between vet and nonvet salaries, the corellation coefficient is 1.