Linearity

Linear Regression

library(tidyverse)

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library(ggplot2)
library(readxl)

setwd("~/Desktop/Monday Class")
district <- read_excel("district.xls")


model_simple <- lm(DA0912DR21R ~ DPSTURNR, data = district)
summary(model_simple)

## 
## Call:
## lm(formula = DA0912DR21R ~ DPSTURNR, data = district)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -3.727 -1.143 -0.797  0.183 49.326 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)   
## (Intercept)  0.72294    0.24291   2.976  0.00298 **
## DPSTURNR     0.02521    0.01065   2.366  0.01815 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.318 on 1090 degrees of freedom
##   (115 observations deleted due to missingness)
## Multiple R-squared:  0.00511,    Adjusted R-squared:  0.004197 
## F-statistic: 5.598 on 1 and 1090 DF,  p-value: 0.01815

#My Dependent variable is Grades 9–12 Dropout Rate, and my Independent variable is Teacher Turnover Rate.

#My Multiple model for both attendance and college prep shows that Attendance has a stronger effect on Drop Out Rate than College Prep, and that its effect is signficant. My R squared shows that .462 of my model is explained by attendance and college prep courses.

Regression, much like t-tests and correlations, is all about relationships. What is the relationship between X and Y? Or between X, Y and Z?

For very simple data, this is easy enough to see. You can just plot it:

ggplot(district,aes(x= DPSTURNR,y = DA0912DR21R)) + geom_point()

## Warning: Removed 115 rows containing missing values or values outside the scale range
## (`geom_point()`).

#graph 1 looks like there is a relationship with the variables. 
ggplot(district,aes(x= DPSTURNR,y = DA0912DR21R )) + geom_point()

## Warning: Removed 115 rows containing missing values or values outside the scale range
## (`geom_point()`).

#Graph 2 does not look like it has a relationship.