R Markdown
# Reading into the data, finding the dimensions, and finding which variables are discrete and which variables are continuous
spm = read.csv('/Users/aaron/Downloads/spm2022_data.csv')
dim(spm) # 21 variables, 471 observations
## [1] 471 21
summary(spm)
## wt Age Mar Sex
## Min. : 10.00 Min. :20.00 Min. :1.00 Min. :1.000
## 1st Qu.: 53.00 1st Qu.:40.50 1st Qu.:1.00 1st Qu.:1.000
## Median : 77.00 Median :56.00 Median :1.00 Median :2.000
## Mean : 99.94 Mean :54.24 Mean :2.27 Mean :1.505
## 3rd Qu.: 118.50 3rd Qu.:67.00 3rd Qu.:3.00 3rd Qu.:2.000
## Max. :1136.00 Max. :94.00 Max. :5.00 Max. :2.000
## Education Race AGI HI_premium
## Min. :0.000 Min. :1.000 Min. : 0 Min. : 0
## 1st Qu.:2.000 1st Qu.:1.000 1st Qu.: 27648 1st Qu.: 0
## Median :3.000 Median :1.000 Median : 65000 Median : 576
## Mean :2.958 Mean :1.633 Mean : 94878 Mean : 1667
## 3rd Qu.:4.000 3rd Qu.:2.000 3rd Qu.: 115552 3rd Qu.: 2000
## Max. :4.000 Max. :4.000 Max. :1568000 Max. :24000
## Moop_other SPM_PovThreshold SPM_NumPer SPM_NumKids
## Min. : 0.0 Min. :11420 Min. : 1.00 Min. :0.0000
## 1st Qu.: 156.5 1st Qu.:16913 1st Qu.: 1.00 1st Qu.:0.0000
## Median : 540.0 Median :21516 Median : 2.00 Median :0.0000
## Mean : 1170.6 Mean :25050 Mean : 2.48 Mean :0.5563
## 3rd Qu.: 1297.0 3rd Qu.:31361 3rd Qu.: 3.00 3rd Qu.:1.0000
## Max. :15100.0 Max. :86732 Max. :11.00 Max. :7.0000
## SPM_NumAdults SPM_TenMortStatus SPM_Totval SPM_FedTax
## Min. :1.000 Min. :1.000 Min. : 0 Min. : -9757
## 1st Qu.:1.000 1st Qu.:1.000 1st Qu.: 42500 1st Qu.: 0
## Median :2.000 Median :2.000 Median : 81000 Median : 4305
## Mean :1.924 Mean :1.822 Mean : 115727 Mean : 13463
## 3rd Qu.:2.000 3rd Qu.:2.500 3rd Qu.: 133150 3rd Qu.: 12252
## Max. :6.000 Max. :3.000 Max. :1568000 Max. :501798
## SPM_FedTaxBC SPM_EITC SPM_FICA SPM_StTax
## Min. : 0 Min. : 0.0 Min. : 0.0 Min. :-2175
## 1st Qu.: 1283 1st Qu.: 0.0 1st Qu.: 573.5 1st Qu.: 0
## Median : 5697 Median : 0.0 Median : 4590.0 Median : 1070
## Mean : 14864 Mean : 292.5 Mean : 6125.0 Mean : 3291
## 3rd Qu.: 13843 3rd Qu.: 0.0 3rd Qu.: 8989.0 3rd Qu.: 3657
## Max. :499986 Max. :6935.0 Max. :50348.0 Max. :77744
## SPM_CapWkCCXpns
## Min. : 0
## 1st Qu.: 620
## Median : 1612
## Mean : 2126
## 3rd Qu.: 3225
## Max. :24825
# variable name -> definition
# wt -> weight
# mar -> marriage
# AGI -> adjusted gross income
# HI_premium -> Health insurance premium
# Moop_other -> Total medical out of pocket expenditures
# SPM_PovThreshold -> SPM unit's SPM poverty threshold x?
# SPM_NumPer -> SPM unit's number of persons in household x
# SPM_TenMortStatus -> SPM unit's tenure/mortgage status x
# SPM_Totval -> SPM unit's cash income
# SPM_FedTaxBC -> SPM unit's Federal tax before refundable tax credits
# SPM_EITC -> SPM unit's Federal Earned Income Tax Credit
# SPM_FICA -> SPM unit's Federal Insurance Contributions Act and federal retirement contribution
# SPM_StTax -> SPM unit's state tax
# SPM_CapWkCCXpns -> SPM unit's capped work and child care expenses
# Calculating the correlation our two chosen variables, AGI and SPM_FICA
cor(spm$AGI, spm$SPM_FICA)
## [1] 0.7113186
# plotting AGI vs. SPM_FICA, with AGI as the explanatory variable to visually confirm a linear trend
plot(spm$AGI, spm$SPM_FICA,
main = 'AGI vs. FICA',
xlab = 'AGI',
ylab = 'FICA')
# Plotting and calculating summary statistics and standard deviation for AGI
hist(spm$AGI)
summary(spm$AGI)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0 27648 65000 94878 115552 1568000
sd(spm$AGI)
## [1] 133947.7
# Plotting and calculating summary statistics and standard deviation for SPM_FICA
hist(spm$SPM_FICA)
summary(spm$SPM_FICA)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.0 573.5 4590.0 6125.0 8989.0 50348.0
sd(spm$SPM_FICA)
## [1] 6643.309
# Fitting a linear model to our variables with AGI as the explanatory variable
spmod = lm(spm$SPM_FICA ~ spm$AGI)
# Summarizing the different aspects of the linear model to find the slope and intercept of the model
summary(spmod)
##
## Call:
## lm(formula = spm$SPM_FICA ~ spm$AGI)
##
## Residuals:
## Min 1Q Median 3Q Max
## -22351.7 -2806.1 -471.6 2120.7 29188.4
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.778e+03 2.640e+02 10.52 <2e-16 ***
## spm$AGI 3.528e-02 1.610e-03 21.92 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4674 on 469 degrees of freedom
## Multiple R-squared: 0.506, Adjusted R-squared: 0.5049
## F-statistic: 480.3 on 1 and 469 DF, p-value: < 2.2e-16
# Residual plot to look for any clear patterns
plot(spmod$residuals ~ spm$AGI,
main = 'Residual Plot',
xlab = 'AGI',
ylab = 'Residuals')
abline(h = 0,
col = 'red',
lwd = 1.5)
