Correlation refers to the statistical association between two variables
What happens to one variable in a positive correlation when the other increases?
It also increases
A positive correlation can be mathematically represented as y = mx + c
Give an example of a positive correlation.
Height and weight
In a negative correlation, as one variable increases, the other increases.
False
A negative correlation can be mathematically represented as y = -mx + c
Give an example of a negative correlation.
Exercise and body fat
In a zero correlation, the slope m is equal to zero.
In a zero correlation, the mathematical representation is y = c
Give an example of variables with zero correlation.
Shoe size and IQ
Match the correlation type with its relationship:
Positive correlation ↔️ As one variable increases, the other increases
Negative correlation ↔️ As one variable increases, the other decreases
Zero correlation ↔️ No meaningful relationship
What does Pearson's correlation coefficient measure?
Linear relationship strength
A perfect positive correlation has a value of +1
What does a Pearson's r value of 0 indicate?
Zero correlation
A Pearson's r value of -1 indicates a perfect negative correlation.
A study finding r=0.85 between study hours and exam scores indicates a strong positive correlation
What is the range of values for Pearson's correlation coefficient?
-1 to +1
What does a Pearson's r value of +1 signify?
Perfect positive correlation
A Pearson's r value of 0 indicates a zero correlation
What does a Pearson's r value of 0.85 indicate between study hours and exam scores?
Strong positive correlation
What does Pearson's correlation coefficient measure?
Strength and direction of linear relationship
The covariance between two variables is represented by Cov(X,Y)
The standard deviations of X and Y are denoted by σX and σY, respectively.standard
Steps to calculate Pearson's correlation coefficient
1️⃣ Calculate the covariance between X and Y
2️⃣ Calculate the standard deviations of X and Y
3️⃣ Plug these values into the formula
Pearson's correlation coefficient is calculated using the covariance and standard deviations of the variables.
The formula for Pearson's correlation coefficient is r=σXσYCov(X,Y) where Cov(X,Y) represents the covariance
Covariance is a measure of how two variables change together.
What are σX and σY in the formula for Pearson's correlation coefficient?
Standard deviations
Match the steps to calculate Pearson's correlation coefficient with their descriptions:
Calculate the covariance ↔️ Measure how two variables change together
Calculate the standard deviations ↔️ Measure the spread of each variable
Plug values into the formula ↔️ Substitute calculated values into r
Pearson's correlation coefficient ranges from -1 to 1.
Steps to calculate Pearson's correlation coefficient (r)
1️⃣ Calculate the covariance between X and Y
2️⃣ Calculate the standard deviations of X and Y
3️⃣ Plug the values into the formula
Pearson's correlation coefficient is denoted by the symbol r.
What is the formula for Pearson's correlation coefficient?
r=σXσYCov(X,Y)
The covariance between X and Y is represented by \text{Cov}(X, Y)</latex>.
The first step in calculating Pearson's correlation coefficient is to calculate the covariance between X and Y.
Pearson's correlation coefficient measures the strength and direction of a linear relationship between two variables.
The Pearson's correlation coefficient formula is r = \frac{\text{Cov}(X, Y)}{\sigma_{X} \sigma_{Y}}</latex>, where σX and σY are the standard deviations of X and Y.
Match the term with its description:
\text{Cov}(X, Y) ↔️ Covariance between X and Y
\sigma_{X} ↔️ Standard deviation of X
\sigma_{Y} ↔️ Standard deviation of Y
Steps to calculate Pearson's correlation coefficient (r)
1️⃣ Calculate the covariance between X and Y
2️⃣ Calculate the standard deviations of X and Y
3️⃣ Plug the values into the formula
A Pearson's correlation coefficient of 0 indicates no linear relationship between two variables.