Nicolas Cage Research Part 3 – Are Nicolas Cage movies getting worse?

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In order to determine if films with Cage are getting worse, comparisons of his movies over time will be necessary. A lot of this has already been touched on in previous sections, but it will be done with a bit more rigour here. There are several ways of judging a movie, and using only one of them might not give the most reliable results. So to properly judge film performance over time, a way of comparing all of them at once has been devised. This is called The Cage Coefficient.

The Cage Coefficient is a weighted average of various key performance indicators after they have been normalised in order to show how that indicator has performed over time relative to itself. The indicators and their respective weights are:

  • Normalised Rotten Tomatoes Rating (0.175 Weighting)
  • Normalised IMDB Rating (0.175 Weighting)
  • Normalised Total IMDB Ratings (0.325 Weighting)
  • Normalised Film Profit (0.325 Weighting)
This provides an indicator of film performance as the aggregate of what people think of it, how many people have seen it and whether it was a financial success. It is presented below: CageCoeff The value of the Cage Coefficient can then be used in a Linear Regression with the following equation:

{\large \textit{CageCoefficient} = \beta_0 + \beta_1 (\textit{MovieNumber}) + \mu}

This will be used to test two hypotheses:
  • Have Nicolas Cage Movies been getting worse since he first started acting?
  • Have Nicolas Cage Movies been getting worse since his initial breakthrough in the mid 1990’s?

First Hypothesis: Nicolas Cage’s movies have been getting worse since the beginning of his career

For the first case, where every movie Cage has been in is included the equation is as follows:
{\large{\textit{CageCoefficient} = 0.6362 + 0.0105 (\textit{MovieNumber}) }  
That the coefficient on Movie Number is positive says that his films are not getting worse over time. A two sided test will be used to test if this is a statistically significant relationship at the 95% level of significance.

\large{ H_0: \beta_1 = 0 }\beta_1 (coefficient on Movie Number) since his first film has no effect on the Cage Coefficient.
\large{ H_1: \beta_1 \neq 0 }\beta_1 (coefficient on Movie Number) since his first film has an effect on the Cage Coefficient that is statistically different from no effect at all.

\large{T_{stat} = 0.0105/0.006104 = 1.7233} 
\large{T_{crit} = T_{0.975,61-2} = 2.001}  

Since  T_{stat}  is not greater than  T_{crit}  for a two sided T-Test, the null hypothesis cannot be rejected. We can therefore conclude that at the 95% level of significance there is insufficient evidence to suggest that Nicolas Cage’s movies have been getting either better or worse since the beginning of his career. Surprised?

Second Hypothesis: Nicolas Cage’s movies have been getting worse since 1995

For the second case, where only movies after Leaving Las Vegas (his initial breakthrough) are included the equation for the Cage Coefficient is as follows:
\large{\textit{CageCoefficient} = 0.2415 - 0.0273 (\textit{MovieNumber})  
Unlike the previous case, we can notice immediately that the coefficient on Movie Number is negative. As to whether it is significant, we can use a one sided test T Test.

\large{ H_0: \beta_1 = 0 }\beta_1 (coefficient on Movie Number) since Leaving Las Vegas has no effect on the Cage Coefficient.
\large{ H_1: \beta_1 < 0 }\beta_1 (coefficient on Movie Number) since Leaving Las Vegas has a negative effect on the Cage Coefficient.

\large{T_{stat} = 0.0273/0.013419 = -2.0344}  
\large{T_{crit} = T_{0.975,61-2} = -1.686}  

Since T_{stat} is less than T_{crit} for a one sided T-Test the null hypothesis can be rejected. We can then conclude that at the 95% level of significance there is sufficient evidence that the Cage Coefficient has been decreasing since his initial breakthrough in the mid 1990’s with Leaving Las Vegas. If the Cage Coefficient is an accurate representation of the quality of a movie then it would seem that Nicolas Cage movies have been getting worse in more recent years.

To a lot of people this probably comes as no surprise, but I am actually pretty surprised to find this result. I know Cage has had his ups and downs but I really wasn’t expecting there to be a statistically significant downward trend. The more you know!

Up Next…

The next post is going to conclude this short series and summarise what we’ve learnt about Nicolas Cage. There might even be a few bold predictions about where he might go in future years too!

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