HW 6

library(tidyverse)

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Linear Regression

I am using my Texas Department of Family and Protective Services dataset to examine how fiscal year and victim confirmation status relate to the number of victims.

Loading the Data

dfps_data <- read.csv("dfps_data.csv", check.names = FALSE)
head(dfps_data)

##   Fiscal Year Program     County    Region Confirmed Victims # of Victims
## 1        2025     DCI Hutchinson 1-Lubbock     Not Confirmed            1
## 2        2025     DCI    Lubbock 1-Lubbock     Not Confirmed           36
## 3        2025     DCI    Lubbock 1-Lubbock  Confirmed Victim            4
## 4        2025     DCI  Ochiltree 1-Lubbock     Not Confirmed            1
## 5        2025     DCI     Potter 1-Lubbock     Not Confirmed           13
## 6        2025     DCI     Potter 1-Lubbock  Confirmed Victim            1

str(dfps_data)

## 'data.frame':    3121 obs. of  6 variables:
##  $ Fiscal Year      : int  2025 2025 2025 2025 2025 2025 2025 2025 2025 2025 ...
##  $ Program          : chr  "DCI" "DCI" "DCI" "DCI" ...
##  $ County           : chr  "Hutchinson" "Lubbock" "Lubbock" "Ochiltree" ...
##  $ Region           : chr  "1-Lubbock" "1-Lubbock" "1-Lubbock" "1-Lubbock" ...
##  $ Confirmed Victims: chr  "Not Confirmed" "Not Confirmed" "Confirmed Victim" "Not Confirmed" ...
##  $ # of Victims     : chr  "1" "36" "4" "1" ...

Preparing the Data

The number of victims variable must be numeric for regression analysis.

dfps_data$`# of Victims` <- as.numeric(dfps_data$`# of Victims`)

## Warning: NAs introduced by coercion

dfps_data$`Confirmed Victims` <- as.factor(dfps_data$`Confirmed Victims`)
regression_data <- dfps_data %>%
  select(`# of Victims`, `Fiscal Year`, `Confirmed Victims`)
regression_data <- na.omit(regression_data)

Creating the Linear Model

victim_model <- lm(`# of Victims` ~ `Fiscal Year` + `Confirmed Victims`,
                   data = regression_data)

Summary of the Linear Model

summary(victim_model)

## 
## Call:
## lm(formula = `# of Victims` ~ `Fiscal Year` + `Confirmed Victims`, 
##     data = regression_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -28.93 -22.13  -7.62  -0.34 895.21 
## 
## Coefficients:
##                                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)                      -1670.3258   648.8012  -2.574  0.01008 *  
## `Fiscal Year`                        0.8295     0.3211   2.583  0.00984 ** 
## `Confirmed Victims`Not Confirmed    20.6207     1.9741  10.446  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 51.4 on 3113 degrees of freedom
## Multiple R-squared:  0.03571,    Adjusted R-squared:  0.03509 
## F-statistic: 57.65 on 2 and 3113 DF,  p-value: < 2.2e-16

The R-squared value shows how much variation in victim counts is explained by the model. The coefficient p-values show which predictors are statistically significant.

Interpreting the Results

In my model output, fiscal year and confirmed victim status were statistically significant predictors at the 0.05 level. The model’s R-squared was approximately 0.0357, meaning it explained about 3.57% of the variation in victim counts.

The fiscal year estimate was approximately 0.8295, indicating a small positive association with victim counts when confirmation status is held constant. The estimate for “Not Confirmed” was approximately 20.6207 higher than the reference category, “Confirmed Victim,” when fiscal year is held constant.

Testing the Assumption of Linearity

plot(victim_model, which = 1)

The residuals-versus-fitted plot helps assess whether the linearity assumption is reasonable. A random scatter around zero supports linearity, while a curved pattern suggests that the assumption may be violated.