Lecture 36- Correlation

Question 1

What does the correlation coefficient (r) summarize?

Answer 1

The strength of a linear relationship between variables as well as the direction of this relationship

Question 2

How do you interpret r i.e. what values mean what?

Answer 2

• r is always between -1 to +1
• A positive r value means Y and X increase together
• A negative r value means as Y increases X decreases (and vice versa: basically what ever one variable does the other variable is doing the opposite thing).

Question 3

What does r=0 mean?

Answer 3

There is no linear relationship between the variables

Question 4

What does a strong/ weak relationship look visually?

Answer 4

• Weak= more scatter

- Strong= Points clustered heavily around the line of best fit

Question 5

Calculate the correlation coefficient using the data on slide 694 and the equation found here (don’t need to memorize)?

Answer 5

Answers on slide

Question 6

What function in r calculates the correlation coefficient?

Answer 6

cor(x,y)

Question 7

How do you set up data in r?

Answer 7

x=c(data)
y=c(data)

Note: can use = or a backwards arrow

Question 8

What is S subscript xy?

Answer 8

The sample covariance between x and y

Question 9

What can the correlation coefficient ‘r’ be rewritten as?

Answer 9

S(subscript xy)/ Sx times Sy

Note: Sx and Sy are the sample standard deviations for the x and y variables

Question 10

Can a correlation coefficient be used for prediction? Why or why not?

Answer 10

No, because its not a model

Question 11

What is meant by the statement that the correlation coefficient is symmetric in variables?

Answer 11

Correlation between x and y is the same as correlation between y and x

Question 12

What is R^2?

Answer 12

• The coefficient of determination: how well does our regression model describe the data
• Is the squared correlation between the observed and predicted responses

Question 13

How do you interpret R^2 i.e. what does the numbers mean?

Answer 13

• Close to 1= regression model describes the data well
• Low value (close to 0) indicates a regression that describes the data poorly

(can only be between 0 and 1, not such thing as a negative R squared value because squaring by nature removes negative signs)

Question 14

What does the total sum of squares describe in contrast to R^2?

Answer 14

• Total sum of squares (TSS)= overall variation in the response variable
• R^2 is instead the proportion of variation in the response that is explained by the predictor variable i.e. how good our model is

Question 15

What is the residual sum of squares (RSS)?

Answer 15

• The total variation of the data points about the regression line i.e how far are our measured y values from the prediction (according to our fitted model)
• In other words RSS is the variation not explained by the regression model

Question 16

What is ESS equal to? What does ESS stand for?

Answer 16

ESS= TSS- RSS

ESS= explained sum of squares. The amount of variation explained by the regression model

Question 17

Complete the sentence: correlation does not equal…

Answer 17

causation

Question 18

Find R squared for the stress data on slide 702

Answer 18

Answers on slide