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LAB 4D: Interpreting Correlations

Lab 4D - Interpreting correlations

Directions: Follow along with the slides, completing the questions in blue on your computer, and answering the questions in red in your journal.

Some background...

  • So far, we’ve learned about measuring the success of a model based on how close its predictions come to the actual observations.

  • The correlation coefficient is a tool that gives us a fairly good idea of how these predictions will turn out without having to make predictions on future observations.

  • For this lab, we will be using the movie data set to investigate the following questions:

    Which variables are better predictors of a movie's critics_rating when the predictions are made using a line of best fit?

Correlation coefficients

  • The correlation coefficient describes the strength and direction of the linear trend.

  • It's only useful when the trend is linear and both variables are numeric.

  • Are these variables linearly related? Why or why not?

Correlation review I

  • Correlation coefficients with values close to 1 are very strong with a positive slope. Values close to -1 means the correlation is very strong with a negative slope.

  • Does this plot have a positive or negative correlation?

Correlation review II

  • Recall that if there is no linear relation between two numerical variables, the correlation coefficient is close to 0.

  • What do you guess the correlation coefficient will be for these two variables?

The movie data

  • Load the movie data using the data command.

  • The data comes from a variety of sources like IMDB and Rotten Tomatoes.

    – The critics_rating contains values between 0 and 100, 100 being the best.

    – The audience_rating contains values that range between 0 and 10, 10 being the best.

    – n_critics and n_audience describe the number of reviews used for the ratings.

    – gross and budget descibes the amount of money the film made and took to make.

Calculating Correlation Coefficients!

  • We can use the cor() function to find the particular correlation coefficient of the variables from the previous plot, which happen to be audience_rating and critics_rating.

    – But note, the cor() function removes any observations which contain an NA value in either variable.

    – Calculate the correlation coefficient for these variables using the cor function. The inputs to the functions work just like the inputs of the xyplot function.

Now answer the following.

  • What was the value of the correlation coefficient you calculated?

  • How does this actual value compare with the one you estimated previously?>/span

  • Does this indicate a strong, weak, or moderate association? Why?

  • How would the scatterplot need to change in order for the correlation to be stronger?

  • How would it need to change in order for the correlation to be weaker?

Correlation and Predictions

  • Find the two variables that look to have the strongest correlation with critics_rating.

    – Compute the correlation coefficients for critics_rating and each of the two variables.

    – Use the correlation coefficient to determine which variable has a stronger linear relationship with critics_rating.

  • Fit two lm models to predict critics_rating with each variable and compute the MSE for each.

    – Use the MSE to determine which variable is a better predictor of critics_rating.

  • How are the correlation coefficient and the MSE related?

On your own

  • Select two different numerical variables from the movie data. Plot the variables using the xyplot() function.

    – Would calculating a correlation coefficient for the two variables be appropriate? Justify your answer.

    – Predict what value you think the correlation coefficient will be. Compare this value to the actual value. Finally, interpret what the actual correlation coefficient means.

  • Work with your classmates to determine which two variables have the strongest correlation coefficient.

    • Why do you think these variables are so strongly related? Is using the correlation coefficient to describe the relationship appropriate and why/why not?