• Linear Regression can be seen in many forms of topics
• The most popular place where Linear Regression is seen is in Computer Science. I though this was the perfect topic to explore as Machine Learnining is a huge part of technology these days and I am a computer science student.
  • It has been seen in machine learning as it is an algorithm that can have the machine lean from datasets and predict the behavior based off of the data points.
  • Examples:
    1. Prediction of student test scores based off of study hours and methods
    2. Checking the error between predicted and actual score
    (From GeeksforGeeks ML and linear regression website)

So what I looked into was how we can come up with a simple equation when it comes to predicting a score.

From Videos:

• A Basic equation for finding a test score is:
  
  

  \(\text{Test Score} = \beta_0 + \beta_1 \cdot \text{Study Hours} + \varepsilon, \; \varepsilon \sim \mathcal{N}(0, 8^2)\)

Where:

\(\beta_0 = \text{starting score}\)

\(\beta_1 = \text{the number the score increases per the hour studied}\)

• A Specific equation for finding a test score if the score increase would be 5 points for every hour:

\(\text{if (}\beta_1 = \text{5), then}\)

\(\text{Test Score} = \beta_0 + 5 \cdot \text{Study Hours} + \varepsilon \;\)

• For predicting student score using Linear Regression

• This is the code that produce the plot from the previous slide:

#From Notes:
fig <- plot_ly(x=x, y=y, type="scatter", mode="markers", name="Test Scores",
        width=800, height=430) %>%add_lines(x = x, y = fitted(mod), name="fitted") %>%
        layout(xaxis = xax, yaxis = yax) %>% layout(margin=list(l=80,r=50,b=40,
            t=40))

\(\text{Error} = b0 - \hat{b0}\;\)

Where:

\(\text{b0} = \text{actual score}\)

\(\hat{b0} = \text{score that was predicted}\)

• The smaller the error, the more accurate the prediction was

-These are the websites that helped me with the code for the math equations and plots:

• https://canvas.asu.edu/courses/249777/pages/module-4-learning-materials?module_item_id=18839986

• https://math.la.asu.edu/~samara/RandPy-lectures/confidence-intervals-for-beta-0-and-beta-1.html

• https://math.la.asu.edu/~samara/RandPy-lectures/gg.html

• https://math.la.asu.edu/~samara/RandPy-lectures/examples.html

• https://medium.com/number-around-us/crafting-elegant-scientific-documents-in-rstudio-a-latex-and-r-markdown-tutorial-a5b788d8a38d

• https://www.geeksforgeeks.org/machine-learning/ml-linear-regression/

• https://www.geeksforgeeks.org/r-language/adding-error-bars-to-a-line-graph-with-ggplot2-in-r/