library(tidyverse)
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library(readxl)
districts <- read_excel("district.xls")
cleaned_districts <- districts |> drop_na()
cleaned_districts_multiple <- lm(DAGC4X21R~DPFPAHSAP+DZCAMPUS+DPETECOP, data=cleaned_districts)
summary(cleaned_districts_multiple)
## 
## Call:
## lm(formula = DAGC4X21R ~ DPFPAHSAP + DZCAMPUS + DPETECOP, data = cleaned_districts)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -70.938  -1.458   0.779   2.879  10.120 
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 100.21309    1.05366  95.110  < 2e-16 ***
## DPFPAHSAP    -0.68293    0.96571  -0.707   0.4800    
## DZCAMPUS     -0.02947    0.01314  -2.243   0.0256 *  
## DPETECOP     -0.09734    0.01742  -5.589 4.92e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.729 on 319 degrees of freedom
## Multiple R-squared:  0.1158, Adjusted R-squared:  0.1075 
## F-statistic: 13.92 on 3 and 319 DF,  p-value: 1.493e-08

Explanation of Data

The Adjusted R-squared indicates about 11% of the model is explained, and with a significantly low p-value there is enough evidence to reject the null hypothesis. Additionally when the significant independent variables, like district size (DZCAMPUS) and the percentage of economically disadvantaged students within a district (DPETECOP), increase by 1, the dependent variable goes down by 0.02947 and 0.09734, respectively.

plot(cleaned_districts_multiple,which=1)

Showing the Work

As the plot illustrates, the relationship betwen the dependent and independent variables is linear.