library(tidyverse)
## Warning: package 'ggplot2' was built under R version 4.4.3
library(pastecs)
## Warning: package 'pastecs' was built under R version 4.4.3
library(ggplot2)

library(lubridate)

options(scipen = 999)#removes scientific notation
library(readxl)
veteran <- read_excel("VA_National_2001-2022_Appendix_508 (1).xlsx",  sheet = "Veteran", range = "A2:N24")
                                                  
colnames(veteran)[9]<-"male.crude.per.100k"                                                  
vets<-lm(`Female Crude Rate per 100,000`~`Year of Death`+male.crude.per.100k+`Population Estimate`,data=veteran)

Focusing on female veteran suicide rate per 100k and looking by year at the male veteran suicide rate. also the size of the state per population.

summary(vets)
## 
## Call:
## lm(formula = `Female Crude Rate per 100,000` ~ `Year of Death` + 
##     male.crude.per.100k + `Population Estimate`, data = veteran)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0971 -0.6698 -0.1397  0.6884  2.6304 
## 
## Coefficients:
##                              Estimate      Std. Error t value Pr(>|t|)  
## (Intercept)           -3276.579388639  1356.159827445  -2.416   0.0265 *
## `Year of Death`           1.577318821     0.657313802   2.400   0.0274 *
## male.crude.per.100k       0.514787773     0.461130679   1.116   0.2789  
## `Population Estimate`     0.000004527     0.000001873   2.417   0.0265 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.135 on 18 degrees of freedom
## Multiple R-squared:  0.8413, Adjusted R-squared:  0.8149 
## F-statistic: 31.81 on 3 and 18 DF,  p-value: 0.0000002083

Combination of three independant variables explains 81.49% of the variance in female veteran crude suicide rate per 100k. the overall model is significant with a P value of 0.0000002083.

there is a signficant effect of year of death with a P value 0.0274.The coefficient of 1.58 suggests that each additional year results in an average increase in female veteran suicides of 1.58 per 100k.

there is also a signficant effect of population estimate with a P value of 0.0265. The coefficient of 0.000004527 means that for every one additonal person the number of female veteran suicides per 100k increases by this much.Another way to look at this is that this means for every additional million people in a state, the female veteran suicide rate increases by 4.5 per 100k.

there is no effect of male veteran crude suicide rate.

plot(vets, which=1)

the plot shows some concerning curvature that might imply that the assumption of linearity is violated. I would want to check the other assumptions to see if I can trust the results of this regression model.