7.4.1 Analysis of Relationships Between Variables

    Cards (86)

    • 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 mm 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 rr value of 0 indicate?

      Zero correlation
    • A Pearson's rr value of -1 indicates a perfect negative correlation.
    • A study finding r=r =0.85 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 rr value of +1 signify?

      Perfect positive correlation
    • A Pearson's rr value of 0 indicates a zero correlation
    • What does a Pearson's rr 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)\text{Cov}(X, Y)
    • The standard deviations of XX and YY are denoted by σX\sigma_{X} and σY\sigma_{Y}, respectively.standard
    • Steps to calculate Pearson's correlation coefficient
      1️⃣ Calculate the covariance between XX and YY
      2️⃣ Calculate the standard deviations of XX and YY
      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=r =Cov(X,Y)σXσY \frac{\text{Cov}(X, Y)}{\sigma_{X} \sigma_{Y}} where Cov(X,Y)\text{Cov}(X, Y) represents the covariance
    • Covariance is a measure of how two variables change together.
    • What are σX\sigma_{X} and σY\sigma_{Y} 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 rr
    • Pearson's correlation coefficient ranges from -1 to 1.
    • Steps to calculate Pearson's correlation coefficient (rr)

      1️⃣ Calculate the covariance between XX and YY
      2️⃣ Calculate the standard deviations of XX and YY
      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=r =Cov(X,Y)σXσY \frac{\text{Cov}(X, Y)}{\sigma_{X} \sigma_{Y}}
    • The covariance between XX and YY is represented by \text{Cov}(X, Y)</latex>.
    • The first step in calculating Pearson's correlation coefficient is to calculate the covariance between XX and YY.
    • 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\sigma_{X} and σY\sigma_{Y} are the standard deviations of XX and YY.
    • Match the term with its description:
      \text{Cov}(X, Y) ↔️ Covariance between XX and YY
      \sigma_{X} ↔️ Standard deviation of XX
      \sigma_{Y} ↔️ Standard deviation of YY
    • Steps to calculate Pearson's correlation coefficient (rr)

      1️⃣ Calculate the covariance between XX and YY
      2️⃣ Calculate the standard deviations of XX and YY
      3️⃣ Plug the values into the formula
    • A Pearson's correlation coefficient of 0 indicates no linear relationship between two variables.
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