• Linear regression is to see if two things are related
• It draws a line through the data that shows which way it trends
• Example: Does budget affect the rating of a movie?

\[\hat{y} = \beta_0 + \beta_1 x\]

• where \(\hat{y}\) is the predicted value
  • in our case the “rating” of the movie
• \(x\) is the predictor
  • budget
• \(\beta_0\) is the intercept
• \(\beta_1\) is the slope of the line

\[\sum_{i=1}^{n} (y_i - \hat{y}_i)^2\]

• For each dot, it finds the gap between the real rating and the line’s guess
  • this is called the residual
• It squares each gap so that they are all positive in case there are any negatives
• Then it adds them up and the best line comes out with the smallest total

• We will be using the data from IMDB (ggplot2movies package)

  • This will be a total of 58788 movies

• Does the budget affect the rating of a movie?

• We’ve only kept movies that have a budget

  • The movies with no budget would not be on the chart

• This leaves us with 5183 movies

• A bigger budget does not seem to guarantee a better rating

graph <- lm(rating ~ log10(budget), data = budgetOfMovie)

form <- coef(graph)
names(form) <- c("Intercept", "Slope")

form

##  Intercept      Slope 
##  6.7657534 -0.1008903

• The slope comes out negative
  • meaning higher budget predicts a slightly lower rating