Video games before and after release get professional reviews from many sites.
The question is: Is a game critic’s score associated with the number of sales?

We will examine:
Critic Score - aggregate professional review score
Global Scales - worldwide sales, measured in millions

We will use Simple Linear Regression

Important: A relationship between critic scores and sales does not establish that higher reviews cause higher sales.

The dataset contains video game sales and review information for games across multiple platforms.

Important variables are: Name
Platform
Genre
Year_of_Release
Critic_Score
User_Score
Global_Sales

For the regression analysis, games without a critic score or global sales value are removed

## Games in original dataset: 16719

## Games used in regression: 8137

First Look at the relationship

There is a substantial variation in sales for every critic score.
Most games have low global sales.
A small number of games have extremely high sales.
The relationship does not appear to be perfectly linear.

A simple linear regression can be written as:

\[ Y_i = \beta_0 + \beta_1X_i + \epsilon_i \]

For this dataset:

\[ \text{Global Sales}_i = \beta_0 + \beta_1(\text{Critic Score}_i) + \epsilon_i \]

Where:

\(\beta_0\) = predicted sales when critic score is 0
\(\beta_1\) = expected change in sales for a one-point increase in critic score
\(\epsilon_i\) = unexplained variation

## 
## Call:
## lm(formula = Global_Sales ~ Critic_Score, data = games_reg)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -1.450 -0.614 -0.284  0.152 81.616 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  -1.517566   0.098569  -15.40   <2e-16 ***
## Critic_Score  0.031995   0.001401   22.84   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.761 on 8135 degrees of freedom
## Multiple R-squared:  0.06026,    Adjusted R-squared:  0.06014 
## F-statistic: 521.6 on 1 and 8135 DF,  p-value: < 2.2e-16

\[ \hat{\beta}_0 + \hat{\beta}_1(\text{Critic Score}) \]

##  (Intercept) Critic_Score 
##  -1.51756611   0.03199472

Intepreting the Slipe

The estimated slope represents the expected change in global sales, in millions of copies, associated with each single point increase in critic score.

This is an association, not causal effect

The distribution is highly right-skewed

A few games sell dramatically more than most.
This creates a problem for ordinary linear regression as the outliers have a large amount of influence on the fitted line.

\[ Y^* = \log_{10}(Y) \]

Therefore: \[ \beta_0 + \beta_1(\text{Critic Score}) + \epsilon \] This allows differences between very small and very large sales values to be represented more proportionally.

## Original-scale R-squared: 0.0603

## Log-scale R-squared: 0.1444

The Log transformation reduces the massive outliers of the blockbuster games and can amke the overall relationship easier to examine

Critic Score x User Score x Global Sales

The 3D visualization helps us see whether games with both high criter and user scores are in different parts of sales distribution.

Are the regression erros reasonably distributed?

A residual is: \[ e_i = y_i - \hat{y}_i \] It represents the difference between an observed and predicted value by the regression model.

The residual plot helps identify:
Non linearity
Unequal variance
Unusually influential Observations

The strong spread of residuals at higher sales is exactly what we expect with the extreme skewed sales of certain games.

What does the model predict for a game scoring 85?

We can use the fitted regression model to calculate a predicted global sales value.

##        fit       lwr      upr
## 1 1.201985 -2.250966 4.654936

The prediction estimates the model’s estimate of roughly 1.2 million global sales for a game with a critic score of 85.

This should not be interpreted as how many copies a game would actually sell.

What did we learn?

Critic score and global sales are able to be examined using simple linear regression
The raw sales data is highly skewed to the right due to a small number of games selling exceptionally well
A logarithmic transformation provides another way to examine the relationship
The regression describes association, not causation
Critic score alone is not enough to explain variation in sales of video games.

Final takeaway

Review scores provide some information about video games, but sales are influenced by many other factors.