J.Graffeo: Linear Regression Discussion

suppressPackageStartupMessages(library(UsingR))
suppressPackageStartupMessages(library(dplyr))
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(tidyr))
suppressPackageStartupMessages(library(knitr))

homes <- as.data.frame(homedata)

head(homes)

hp <- 
  ggplot(homes, aes(x = y1970, y = y2000)) +
  geom_point(size = 1, color = "purple2") +
  geom_smooth(method = lm, se = FALSE, color = "black") +
  xlab("Home Value in 1970") +
  ylab("Home Value in 2000")

hp

## `geom_smooth()` using formula 'y ~ x'

modelh <- lm(y2000 ~ y1970, data = homes)

summary(modelh)

## 
## Call:
## lm(formula = y2000 ~ y1970, data = homes)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -416665  -36308     809   34372  536605 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -1.040e+05  2.337e+03  -44.51   <2e-16 ***
## y1970        5.258e+00  3.147e-02  167.07   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 58000 on 6839 degrees of freedom
## Multiple R-squared:  0.8032, Adjusted R-squared:  0.8032 
## F-statistic: 2.791e+04 on 1 and 6839 DF,  p-value: < 2.2e-16

### With every increase in year, home value increases by 5.258e+00 (%).

### The equation is: Home value in 2000 = -1.040e+05 + 5.258e+00 * home value in 1970

predict(modelh, data.frame(y1970 = c(55000, 60000, 65000)))

##        1        2        3 
## 185183.8 211473.6 237763.5

### According to 'modelh', a home valued at $55,000 in 1970 would be worth $185,183.80 in 2000, a home valued at $60,000 would be worth $211,473.60 in 2000, and a home valued at $65,000 in 1970 would be worth $237,763.50 in 2000.