• Perform Linear Regression
• Use in-built ‘Trees’ data set
• Create Interactive plots

• Checking for missing values (na-values)

n_og = nrow(trees)
per_col = sapply(trees, function(x) sum(is.na(x)))
total_na = sum(per_col)

print(per_col)

##  Girth Height Volume 
##      0      0      0

cat("\nTotal missing values in dataset:", total_na, "\n\n")

## 
## Total missing values in dataset: 0

# There are Zero Missing Values in the data set

\[ y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + \varepsilon_i,\qquad \varepsilon_i\sim\mathcal{N}(0,\sigma^2), \]

where y = Volume, x1 = Girth, x2 = Height.

Matrix form and least squares estimator:

\[ \mathbf{Y} = \mathbf{X}\boldsymbol{\beta} + \boldsymbol{\varepsilon}, \qquad \hat{\boldsymbol{\beta}} = (\mathbf{X}^\top\mathbf{X})^{-1}\mathbf{X}^\top\mathbf{Y}. \]

These give the fitted coefficients used for prediction and inference.

p_plotly <- plot_ly(data = trees, x = ~Girth, y = ~Volume,
        text = ~paste("Girth:", Girth, "<br>Volume:", 
                      Volume, "<br>Height:", Height),
        color = ~Height, colors = c("blue", "red")) %>%
  add_markers(marker = list(size = 7, opacity = 0.7), 
              hoverinfo = "text") %>%
  layout(title = "Girth vs Volume (color = Height)",
         xaxis = list(title = "Girth (in)"),
         yaxis = list(title = "Volume (cubic ft)"))