Question

The data frame `x77` contains data from each of the fifty United States. First coerce the `state.x77` variable into a data frame with:*

```{r, eval=FALSE}
x77 <- data.frame(state.x77)
```

*For the following, make a scatter plot with the regression line:*

1. *The model of illiteracy rate (`Illiteracy`) modeled by high school graduation rate (`HS.Grad`).*

2. *The model of life expectancy (`Life.Exp`) modeled by the murder rate (`Murder`).*

3. *The model of income (`Income`) modeled by the illiteracy rate (`Illiteracy`).*

*Write a sentence or two describing any relationship for each fo the relationships examined above. In particular, do you find it as expected or surprising?*

Please provide code from R and answer all the questions.

Answer 1

Solution:

x77 <- data.frame(state.x77)

library(ggpubr)
require(ggpubr)
ggscatter(x77, x = "HS.Grad", y = "Illiteracy", add = "reg.line") +
stat_cor(label.y = 300) +
stat_regline_equation(label.y = 280)

There exists a a negative relationship between HS Grad and Illiteracy.

as Illiteracy increases,,HS grad decreases.

Rgression eq is

illiteracy=3.8-0.05*HS Grad

R=-0.66

p=2.2*10^-7

p<0.05

Relationship between HS Grad and Illiteracy. is statistically significant at 5% level of signfiicance

Solution2:

ggscatter(x77, x = "Murder", y = "Life.Exp", add = "reg.line") +
stat_cor(label.y = 300) +
stat_regline_equation(label.y = 250)

Life expectancy =73-0.28*Murder

there exists a negative relationship between murders and life expectancy.

As number of murders increases,life expectancy decreases and vice versa.

R=-0.78

p=2.3*01^-11

p<0.05

Relationship between HS Grad and Illiteracy. is statistically significant at 5% level of signfiicance

3. *The model of income (`Income`) modeled by the illiteracy rate (`Illiteracy`).*

ggscatter(x77, x = "Illiteracy", y = "Income", add = "reg.line") +
stat_cor(label.y = 400) +
stat_regline_equation(label.y = 50)

Regression eq is

income=5000-440*Illiteracy

There exists a negative relationship between Income and Illiteracy

as Illiteracy rate is high,income earned is low and viceversa

r=-0.44

p=0.0015

p<0.05

Relationship between income and Illiteracy. is statistically significant at 5% level of signfiicance