Atividade regressão

library(readr)
income_data <- read_csv("income.data.csv")

## New names:
## Rows: 498 Columns: 3
## ── Column specification
## ──────────────────────────────────────────────────────── Delimiter: "," dbl
## (3): ...1, income, happiness
## ℹ Use `spec()` to retrieve the full column specification for this data. ℹ
## Specify the column types or set `show_col_types = FALSE` to quiet this message.
## • `` -> `...1`

#View(income_data)

cor(income_data$happiness, income_data$income)

## [1] 0.8656337

Simple_Regression = lm( income_data$income ~ income_data$happiness)

summary(Simple_Regression)

## 
## Call:
## lm(formula = income_data$income ~ income_data$happiness)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -2.94796 -0.57730  0.02277  0.55661  2.23185 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            0.90533    0.10039   9.018   <2e-16 ***
## income_data$happiness  1.04973    0.02726  38.505   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8708 on 496 degrees of freedom
## Multiple R-squared:  0.7493, Adjusted R-squared:  0.7488 
## F-statistic:  1483 on 1 and 496 DF,  p-value: < 2.2e-16

plot(income_data$happiness, income_data$income)
abline(Simple_Regression, col = "red", lwd = 2 )

anova(Simple_Regression)

## Analysis of Variance Table
## 
## Response: income_data$income
##                        Df  Sum Sq Mean Sq F value    Pr(>F)    
## income_data$happiness   1 1124.32 1124.32  1482.6 < 2.2e-16 ***
## Residuals             496  376.13    0.76                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

qf(0.95, 1,496)

## [1] 3.860275