GLM, IMDB assignment

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This is a Draft

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Assignment

• Make a descriptive analysis to look at the relationship between the covariates and the profit. Covariates used in this analysis are content_rating, budget, director_facebook_likes.
  
• Model the profit as a function of budget only, use the following techniques:
  

1. Polynomial regression model
2. Truncated polynomial splines of degree 2 (consider k=2, 3 and 5 knots)
3. B-splines of degree 2 (consider m=3, 5 and 8 knots)
4. Cubic P-splines (consider k=5, 8 and 20 knots)

• Include the other covariates in the model and determine what variables show an impact on the profit.
  
• A movie is defined successful when the profit is positive. Fit a model that relates the probability of success and the covariates considered above.

Descriptive

Should we add a dummy to know if the movie turned a profit or not?

Distribution of Budgets

Min.	1st Qu.	Median	Mean	3rd Qu.	Max.
8.00	32.00	50.00	65.96	80.00	300.00

Models

Budget only

For some help with poly in R I used this link
For help on the cubic splines I used: link

plot(budget,profit,col="grey",xlab="Budget",ylab="Profit", main = "We want to predict profit by only using budget")+
  abline(h=0, col = "green")

## integer(0)

b.3<-lm(profit ~ bs(budget,knots = 2),data = train)
b.5 <- lm(profit ~ bs(budget,knots = 5),data = train)
b.8 <- lm(profit ~ bs(budget,knots = 8),data = train)

b.donaldcuts <- lm(profit ~ bs(budget,knots = c(32,50,65.96,80)),data = train)

AIC(poly.3,b.5,b.8,b.donaldcuts)

All these models have the same AIC except for my model where I used the distribution of budget to define where to cut. The value is still quite close. Looks strange.
Let’s look at some residuals