lab 9.Rmd

---
title: "Lab 9"
author: "Netanel Weinstein"
date: "December 2, 2018"
output: 
  html_document:
  toc: true
  toc_depth: 4
---


```{r plot, echo = FALSE}
library(rio)
library(tidyverse)
library(here)
data
data <- import(here("data",  "ecls-k_samp.sav")) %>%
  characterize() %>% 
  janitor::clean_names() %>% 
  mutate(ses_cat = factor(ses_cat, 
                          levels = c("FIRST QUINTILE",
                                     "SECOND QUINTILE",
                                     "THIRD QUINTILE",
                                     "FOURTH QUINTILE",
                                     "FIFTH QUINTILE"),
                          labels = c("First",
                                     "Second", 
                                     "Third", 
                                     "Fourth", 
                                     "Fifth")))
  
#recreation of plot:
ggplot(data, aes(x = t1mscale, y = t2mscale))  +
  geom_point(color = "gray") +
  geom_smooth(aes(color = ses_cat),
              method = "lm",
              se = FALSE) +
  ggtitle("Math scores", "Relation from Time 1 to Time 2") +
  xlab("Math Score (time 1)") +
  ylab("Math Score (time 2)")

  
```

**Regression model** for *Math* Achievment:
$$
math_{t2_i} = \alpha + \beta_1(math_{t1_i}) + \beta_2(SES_{cat_i}) + \beta_3(math_{t1_i} \times SES_{cat_i}) \epsilon
$$