Homework 6

knitr::opts_chunk$set(echo = TRUE)

#load packages
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.2.1     ✔ readr     2.2.0
## ✔ forcats   1.0.1     ✔ stringr   1.6.0
## ✔ ggplot2   4.0.3     ✔ tibble    3.3.1
## ✔ lubridate 1.9.5     ✔ tidyr     1.3.2
## ✔ purrr     1.2.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(pastecs)

## 
## Attaching package: 'pastecs'
## 
## The following objects are masked from 'package:dplyr':
## 
##     first, last
## 
## The following object is masked from 'package:tidyr':
## 
##     extract

library(readxl)
library(car)

## Loading required package: carData
## 
## Attaching package: 'car'
## 
## The following object is masked from 'package:dplyr':
## 
##     recode
## 
## The following object is masked from 'package:purrr':
## 
##     some

  district <- read_excel("district.xls")

model1 <- lm(DAGC4X21R~DPFVTOTK+DPETECOP+DPSTTOSA,data=district)
summary(model1)

## 
## Call:
## lm(formula = DAGC4X21R ~ DPFVTOTK + DPETECOP + DPSTTOSA, data = district)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -95.131  -1.181   2.285   5.007  12.955 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  1.079e+02  4.369e+00  24.684  < 2e-16 ***
## DPFVTOTK     1.019e-07  2.625e-07   0.388    0.698    
## DPETECOP    -1.489e-01  1.898e-02  -7.847 1.03e-14 ***
## DPSTTOSA    -9.310e-05  7.660e-05  -1.215    0.224    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 12.45 on 1067 degrees of freedom
##   (136 observations deleted due to missingness)
## Multiple R-squared:  0.05695,    Adjusted R-squared:  0.0543 
## F-statistic: 21.48 on 3 and 1067 DF,  p-value: 1.64e-13

## DAGC4X21R "DPFVTOTK", "DPETECOP", "DPSTTOSA")]
## graduation rate, property wealth, % economically disadvantaged, and average teacher salary.

##Adjusted r squared is .05 which means the model accounts for 5% of the variance in weight. 
##P-value well below 0.05. As a group, the predictors do better than nothing. So the model is real, just weak.
##The variable % economically disadvantaged students is significant
##The two variables: property wealth and average teacher salary are not significant

##Estimates or Beta Coefficient's: 
##For every 1 point increase in economically disadvantaged students, graduation rates drop by about -1.489e-01 or 0.15 points.
##Districts with more low-income students tend to have somewhat lower graduation rates, even after accounting for property wealth and teacher pay. This ##shows a connection, not proof that one causes the other.

plot(model1,which=1)

##The plot shows linearity is only partly met:
##The red line is mostly flat near zero and is slighly tilting downward