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Correlation Coefficient quiz #4

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  • What does correlation measure?
    Correlation measures the extent to which two factors vary together in a linear fashion.
  • How do you find the correlation coefficient for a set of data?
    Enter the data into a calculator and use the linear regression function to calculate r.
  • The correlation coefficient measures only the strength of the _____ between variables.
    Linear relationship.
  • What determines the sign (positive or negative) of a correlation coefficient?
    Whether the variables increase together (positive) or one increases as the other decreases (negative).
  • What is the possible range for the correlation coefficient r?
    r ranges from -1 to 1.
  • What two aspects of a relationship between variables does the correlation coefficient r measure?
    The correlation coefficient r measures both the direction and the strength of the linear relationship between two variables. Direction is indicated by the sign, and strength by how close r is to ±1.
  • How can you visually distinguish between strong and weak correlation on a scatterplot?
    Strong correlation is shown by data points tightly clustered around a straight line, while weak correlation has points more loosely scattered. The closer the points are to the line, the stronger the correlation.
  • What is the first step you should take on a TI-84 calculator before calculating the correlation coefficient?
    You should turn on the 'diagnostic on' feature from the calculator's catalog before calculating the correlation coefficient. This ensures the calculator will display the r value in the output.
  • When using a calculator to find r, which lists are typically used for the x and y data?
    The x data is usually entered into L1 and the y data into L2. These are the default lists used by the calculator's linear regression function.
  • Why should you not confuse the slope of the best fit line with the value of r?
    The slope of the best fit line indicates the rate of change, while r measures how closely the data points cluster around that line. A line can have a steep or shallow slope regardless of the strength of the correlation.
  • When does the correlation coefficient indicate the weakest relationship between two variables?
    The correlation coefficient indicates the weakest relationship when its value is closest to zero.
  • What can a correlation coefficient indicate about the relationship between two variables?
    A correlation coefficient indicates both the direction (positive or negative) and the strength (strong or weak) of the linear relationship between two variables.
  • What value of the correlation coefficient represents the strongest correlation between two variables?
    The strongest correlation is represented by a correlation coefficient (r) value closest to either +1 or -1.
  • Which correlation coefficient value indicates the strongest relationship between two variables?
    A correlation coefficient value closest to +1 or -1 indicates the strongest relationship.
  • What does it mean if the correlation coefficient is negative?
    If the correlation coefficient is negative, it means that as one variable increases, the other variable tends to decrease, indicating a downward trend.
  • In psychology, which correlation coefficient value indicates the strongest relationship between two variables?
    In psychology, as in statistics generally, the strongest relationship is indicated by a correlation coefficient value closest to +1 or -1.
  • Which r-value represents the weakest correlation between two variables?
    The r-value closest to zero represents the weakest correlation.
  • How can you identify the strongest correlation among several correlation coefficients?
    The strongest correlation is identified by the r-value that is closest to +1 or -1.
  • Which r-value represents the weakest correlation in a dataset?
    The r-value closest to zero represents the weakest correlation in a dataset.
  • What is considered the strongest correlation between two variables?
    The strongest correlation is when the correlation coefficient (r) is closest to +1 or -1.
  • What is the strongest possible value for a correlation coefficient?
    The strongest possible value for a correlation coefficient is +1 or -1.
  • What does a negative correlation coefficient mean in statistics?
    A negative correlation coefficient means that as one variable increases, the other variable tends to decrease, showing a negative linear relationship.
  • What is the interpretation of a negative correlation coefficient?
    A negative correlation coefficient indicates a downward trend, meaning that the variables move in opposite directions.
  • Which correlation coefficient value best represents a moderate relationship between two variables?
    A correlation coefficient value around ±0.5 to ±0.7 typically represents a moderate relationship.