plot_ly(x = time(LakeHuron), 
        y = LakeHuron, 
        type = "scatter", 
        mode = "lines+markers") %>%
  layout(title = "Water Level of Lake Huron (1875 - 1972)",
         xaxis = list(title = "Year"),
         yaxis = list(title = "Water Level (Feet)"))

model <- lm(mpg ~ wt, data = mtcars)

ggplot(mtcars, aes(x = wt, y = mpg)) + 
  geom_point(size = 3, color = "blue") + 
  geom_smooth(method = 'loess',formula = 'y ~ x', color = "red", se = F) +
  labs(title = "Relationship Between Weight and MPG",
       x = "Weight (1000 lbs)",
       y = "Miles Per Gallon (MPG)") +
  theme_minimal()

  summary(model)

## 
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.5432 -2.3647 -0.1252  1.4096  6.8727 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  37.2851     1.8776  19.858  < 2e-16 ***
## wt           -5.3445     0.5591  -9.559 1.29e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared:  0.7528, Adjusted R-squared:  0.7446 
## F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10

• Null Hypothesis (\(H_0\)): The mean petal length of setosa is equal to the mean petal length of versicolor.
• Alternative Hypothesis (\(H_a\)): The mean petal length of setosa is not equal to the mean petal length of versicolor.

iris <- datasets::iris
setosa_petal <- iris[iris$Species == "setosa", "Petal.Length"]
versicolor_petal <- iris[iris$Species == "versicolor", "Petal.Length"]
t_test_result <- t.test(setosa_petal, versicolor_petal)
print(t_test_result)

## 
##  Welch Two Sample t-test
## 
## data:  setosa_petal and versicolor_petal
## t = -39.493, df = 62.14, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -2.939618 -2.656382
## sample estimates:
## mean of x mean of y 
##     1.462     4.260

fig <- plot_ly(iris, y = ~Petal.Length, color = ~Species, type = "box") %>%
  layout(title = "Petal Length by Species",
         yaxis = list(title = "Petal Length"),
         xaxis = list(title = "Species"))

fig