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Correlation Coefficient quiz

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  • What does the correlation coefficient (r) measure between two variables?
    It measures the strength and direction of the linear relationship between two variables.
  • What is the range of possible values for the correlation coefficient r?
    The correlation coefficient r ranges from -1 to 1.
  • What does a positive value of r indicate about the relationship between two variables?
    A positive r indicates a positive correlation, meaning as one variable increases, the other also increases.
  • What does a negative value of r indicate about the relationship between two variables?
    A negative r indicates a negative correlation, meaning as one variable increases, the other decreases.
  • What does an r value close to zero signify about the correlation between two variables?
    An r value close to zero signifies weak or no correlation between the variables.
  • How can you visually identify strong correlation in a scatterplot?
    Strong correlation is seen when data points are tightly clustered around a trend line.
  • What r value is generally considered to indicate a strong correlation?
    Generally, r values beyond 0.8 or -0.8 are considered strong correlations.
  • Does the slope of the best fit line affect the value of r?
    No, the slope does not affect r; r depends on how tightly the data points cluster around the line.
  • What is the first step when using a TI-84 calculator to find the correlation coefficient?
    The first step is to turn on 'diagnostic on' in the calculator's catalog menu.
  • Which lists do you use for x and y values when entering data into a TI-84 calculator?
    You use L1 for x values and L2 for y values.
  • Which calculator function do you use to calculate the correlation coefficient on a TI-84?
    You use the 'linreg(ax+b)' function in the calculator's stats menu.
  • Where is the r value displayed in the calculator's output after running linreg(ax+b)?
    The r value is displayed at the very bottom of the calculator's readout.
  • What does an r value of 0.94 indicate about the data's correlation?
    It indicates a strong, positive linear correlation between the variables.
  • What is the difference between r and r squared in the calculator's output?
    r is the correlation coefficient, while r squared is the coefficient of determination; for correlation, use r.
  • What should you do if your data points are not tightly clustered around a trend line?
    Expect a lower r value, indicating weak or no correlation.