Practical_a: code improvement

Practical_a.Rmd

@@ -7,7 +7,7 @@ output:
     use_bookdown: true
     default_style: "light"
     lightbox: true
-    css: "../www/style_Rmd.css"
+    css: "./www/style_Rmd.css"
 
 ---
 
@@ -96,7 +96,6 @@ The data is tidy:
 Meeting these 3 criteria for your data will simplify most of your data processing and analysis.
 
 ```{r}
-dim(penguins)
 summary(penguins)
 ```
 
@@ -255,7 +254,7 @@ With the `mutate()` function create a `diy_pca` tibble with the scaled version o
 <details><summary>Solution</summary>
 <p>
 ```{r}
-diy_pca <- data_f %>% 
+diy_data_f <- data_f %>% 
   mutate(
     bill_length_mm = (bill_length_mm - mean(bill_length_mm)) / sd(bill_length_mm),
     bill_depth_mm = (bill_depth_mm - mean(bill_depth_mm)) / sd(bill_depth_mm),
@@ -284,7 +283,7 @@ point_projection <- function(line_slope, x, y){
   return(list(x = results[1], y = results[2]))
 }
 
-diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     projection_x = point_projection(
@@ -295,7 +294,9 @@ diy_pca %>%
       line_slope = line_slope,
       x = bill_length_mm,
       y = bill_depth_mm)$y
-  ) %>% 
+  )
+
+diy_pca %>% 
   ggplot() +
   geom_point(aes(x = bill_length_mm, y = bill_depth_mm)) +
   geom_abline(slope = line_slope, color = "red") +
@@ -355,7 +356,7 @@ Write the formula to compute the `S_dist` and `Residuals` variables in the `muta
 
 ```{r, eval=F}
 line_slope <- 0.2 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     projection_x = point_projection(
@@ -405,7 +406,7 @@ You can use the `cov()` function to perform this computation
 <details><summary>Solution</summary>
 <p>
 ```{r}
-diy_cov <- diy_pca %>% as.matrix() %>% cov()
+diy_cov <- diy_data_f %>% as.matrix() %>% cov()
 diy_cov
 ```
 </p>
@@ -433,13 +434,12 @@ Then you will need to compute the `slope` value for the `geom_abline` function f
 ```{r include=FALSE}
 point_projection <- function(diy_cov, x, y){
   a <- c(x, y)
-  b <- eigen(diy_cov)$values[1] * eigen(diy_cov)$vector[, 1]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  results <- c(a %*% scaled_b) * scaled_b
+  b <- eigen(diy_cov)$vector[, 1]
+  results <- c(a %*% b) * b
   list(x = results[1], y = results[2])
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc1_x = point_projection(
@@ -475,7 +475,7 @@ point_projection <- function(diy_cov, x, y){
   list(x = results[1], y = results[2])
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc1_x = point_projection(
@@ -494,7 +494,7 @@ diy_pca %>%
   ggplot() +
   geom_point(aes(x = bill_length_mm, y = bill_depth_mm)) +
   geom_abline(slope = , color = "red") + # missing slope value here
-  geom_point(aes(x = projection_x, y = projection_y), color = "red") +
+  geom_point(aes(x = pc1_x, y = pc1_y), color = "red") +
   geom_segment(
     aes(x = bill_length_mm,
         y = bill_depth_mm,
@@ -514,9 +514,8 @@ For the projection function:
 ```{r, eval=F}
 point_projection <- function(diy_cov, x, y){
   a <- c(x, y)
-  b <- eigen(diy_cov)$values[1] * eigen(diy_cov)$vector[, 1]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  results <- c(a %*% scaled_b) * scaled_b
+  b <- eigen(diy_cov)$vector[, 1]
+  results <- c(a %*% b) * b 
   list(x = results[1], y = results[2])
 }
 ```
@@ -542,13 +541,12 @@ Adapt your previous code to perform the computation on the PC2
 ```{r include=FALSE}
 point_projection <- function(diy_cov, x, y){
   a <- c(x, y)
-  b <- eigen(diy_cov)$values[2] * eigen(diy_cov)$vector[, 2]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  results <- c(a %*% scaled_b) * scaled_b
+  b <- eigen(diy_cov)$vector[, 2]
+  results <- c(a %*% b) * b
   return(list(x = results[1], y = results[2]))
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc2_x = point_projection(
@@ -605,7 +603,7 @@ diy_pca %>%
   geom_point(aes(x = bill_length_mm, y = bill_depth_mm)) +
   geom_abline(slope = , color = "red") + # slope of the PC1
   geom_abline(slope = , color = "blue") + # slope of the PC2
-  geom_point(aes(x = projection_x, y = projection_y), color = "blue") +
+  geom_point(aes(x = pc2_x, y = pc2_y), color = "blue") +
   geom_segment(
     aes(x = bill_length_mm,
         y = bill_depth_mm,
@@ -623,9 +621,8 @@ For the projection function:
 ```{r, eval=F}
 point_projection <- function(diy_cov, x, y){
   a <- c(x, y)
-  b <- eigen(diy_cov)$values[2] * eigen(diy_cov)$vector[, 2]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  results <- c(a %*% scaled_b) * scaled_b
+  b <- eigen(diy_cov)$vector[, 2]
+  results <- c(a %*% b) * b
   return(list(x = results[1], y = results[2]))
 }
 ```
@@ -654,13 +651,12 @@ You can merge your previous computation to plot the projection on the 2 first PC
 ```{r include=FALSE}
 point_projection <- function(diy_cov, x, y, PC){
   a <- c(x, y)
-  b <- eigen(diy_cov)$values[PC] * eigen(diy_cov)$vector[, PC]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  results <- c(a %*% scaled_b) * scaled_b
+  b <- eigen(diy_cov)$vector[, PC]
+  results <- c(a %*% b) * b
   return(list(x = results[1], y = results[2]))
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc1_x = point_projection(
@@ -714,7 +710,7 @@ point_projection <- function(diy_cov, x, y, PC){
   # your code
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc1_x = point_projection(
@@ -740,12 +736,11 @@ diy_pca %>%
 ```{r, echo = F}
 point_projection <- function(diy_cov, x, y, PC){
   a <- c(x, y)
-  b <- eigen(diy_cov)$value[PC] * eigen(diy_cov)$vector[, PC]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  a %*% scaled_b
+  b <- eigen(diy_cov)$vector[, PC]
+  a %*% b
 }
 
-diy_pca <- diy_pca %>% 
+diy_pca <- diy_data_f %>% 
   rowwise() %>% # perform the subsequent opperation row by row
   mutate(
     pc1_x = point_projection(
@@ -773,9 +768,8 @@ diy_pca %>%
 ```{r eval=F}
 point_projection <- function(diy_cov, x, y, PC){
   a <- c(x, y)
-  b <- eigen(diy_cov)$value[PC] * eigen(diy_cov)$vector[, PC]
-  scaled_b <- b / c(sqrt(sum(b^2)))
-  a %*% scaled_b
+  b <- eigen(diy_cov)$vector[, PC]
+  a %*% b
 }
 ```
 </p>
@@ -786,14 +780,25 @@ point_projection <- function(diy_cov, x, y, PC){
 In the `prcomp` output you can directly get the coordinates in PCs space from the `$x` slot.
 
 ```{r}
-diy_pca <- diy_pca %>% 
+diy_data_f %>% 
+  rowwise() %>% # perform the subsequent opperation row by row
+  mutate(
+    pc1_x = point_projection(
+      diy_cov = diy_cov,
+      x = bill_length_mm,
+      y = bill_depth_mm,
+      PC = 1),
+    pc2_y = point_projection(
+      diy_cov = diy_cov,
+      x = bill_length_mm,
+      y = bill_depth_mm,
+      PC = 2),
+  ) %>% 
   ungroup() %>% 
   mutate(
     pc1_x_ref = data_f_pca$x[,1],
     pc2_y_ref = data_f_pca$x[,2]
-  )
-
-diy_pca %>% 
+  ) %>% 
   bind_cols(
     data %>% select(-colnames(diy_pca)[1:2]) %>%  filter(sex == "female")
   ) %>%