- Build data frame
age <- c(18, 23, 25, 35, 65, 54,34, 72, 50, 48, 18, 39, 37)
maxHR <- c(200, 189, 189, 185, 170, 175, 185, 168, 170, 175, 205, 190, 178)
df <- data.frame(age, maxHR)
df
## age maxHR
## 1 18 200
## 2 23 189
## 3 25 189
## 4 35 185
## 5 65 170
## 6 54 175
## 7 34 185
## 8 72 168
## 9 50 170
## 10 48 175
## 11 18 205
## 12 39 190
## 13 37 178
- Linear Regression Model
lm_result <- lm(maxHR ~age, data = df)
lm_result
##
## Call:
## lm(formula = maxHR ~ age, data = df)
##
## Coefficients:
## (Intercept) age
## 207.3326 -0.6107
summary(lm_result)
##
## Call:
## lm(formula = maxHR ~ age, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.7994 -3.0660 -0.9594 3.6593 8.6593
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 207.33264 3.71092 55.87 7.45e-15 ***
## age -0.61066 0.08601 -7.10 1.99e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.133 on 11 degrees of freedom
## Multiple R-squared: 0.8209, Adjusted R-squared: 0.8046
## F-statistic: 50.41 on 1 and 11 DF, p-value: 1.992e-05
#This is meaningful model : maxHR = 207.3326 - 0.6107 * age
- Visualization
library(ggplot2)
ggplot(df, aes(age, maxHR))+ geom_point() + xlab("AGE") + ylab(" Maximum Heart Rate") + ggtitle("Relation between Maximum Heart Rate and Age") + stat_smooth()
## `geom_smooth()` using method = 'loess'
ggplot(df, aes(age, maxHR))+ geom_point() + xlab("AGE") + ylab(" Maximum Heart Rate") + ggtitle("Relation between Maximum Heart Rate and Age") + stat_smooth(method = lm, level = 0.85)
