2614 Scatter Plot Transformations Logs

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| By Anthony Nunan
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Anthony Nunan
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Quizzes Created: 132 | Total Attempts: 44,578
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2614 Scatter Plot Transformations Logs - Quiz

Log x and log y transformations


Questions and Answers
  • 1. 

    The log y transformation linearises the scatter plot by :

    • A.

      Turning the y values into log y values

    • B.

      Compressing the y axis values

    • C.

      Stretching the y axis values

    • D.

      Leaving the x axis values the same

    Correct Answer(s)
    A. Turning the y values into log y values
    B. Compressing the y axis values
    D. Leaving the x axis values the same
    Explanation
    The log y transformation linearizes the scatter plot by turning the y values into log y values. This is because taking the logarithm of the y values will spread out the data points that are close together and compress the data points that are far apart, resulting in a more evenly distributed scatter plot. Additionally, the log transformation does not affect the x axis values, so they remain the same.

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  • 2. 

    The log x transformation linearises the scatter plot by :

    • A.

      Changing the x values to log x values

    • B.

      Compressing the x axis values

    • C.

      Stretching the x axis values

    • D.

      Leaving the y values as they are

    Correct Answer(s)
    A. Changing the x values to log x values
    B. Compressing the x axis values
    D. Leaving the y values as they are
    Explanation
    The log x transformation is a mathematical operation that involves taking the logarithm of the x values. This transformation helps to linearize the scatter plot by compressing the x axis values. By taking the logarithm of the x values, the range of the x axis is reduced, making the data points more evenly distributed along the x axis. This compression helps to spread out the data points and make the relationship between the variables more linear. The y values are left unchanged during this transformation.

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  • 3. 

    The scatter plot above will potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer
    A. Log x transformation
    Explanation
    The scatter plot above will potentially be linearized with a log x transformation because it appears to have an exponential relationship between the x and y variables. By taking the logarithm of the x values, the relationship may become more linear, making it easier to analyze and interpret the data.

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  • 4. 

    The scatter plot above will potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer(s)
    A. Log x transformation
    B. Log y transformation
    Explanation
    The scatter plot above will potentially be linearized with log x transformation and log y transformation. These transformations are commonly used when the relationship between the variables in a scatter plot is exponential or logarithmic. By taking the logarithm of the x and y variables, the data points can be spread out more evenly, making it easier to fit a straight line and analyze the linear relationship between the variables.

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  • 5. 

    The scatter plot above will potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer
    B. Log y transformation
    Explanation
    The scatter plot will potentially be linearized with a log y transformation. This means that taking the logarithm of the y-values will help to create a linear relationship between the x and y variables. This transformation is useful when the relationship between the variables is exponential, as taking the logarithm can help to make the relationship more linear.

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  • 6. 

    The scatter plot above will potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer
    C. It is is the wrong quadrant for these transformations
    Explanation
    The scatter plot is in the wrong quadrant for log x or log y transformations. In order for a scatter plot to be linearized using log transformations, the data points should be spread out across all four quadrants. However, in this case, the scatter plot is concentrated in a single quadrant, indicating that log transformations would not be appropriate for linearizing the data.

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  • 7. 

    Which quadrants have potential for a log x transformation

    • A.

      Quadrant 1

    • B.

      Quadrant 2.

    • C.

      Quadrant 3

    • D.

      Quadrant 4

    Correct Answer(s)
    B. Quadrant 2.
    C. Quadrant 3
    Explanation
    A log x transformation is typically used when the data is positively skewed or has a long tail on the right side. Quadrant 2 and Quadrant 3 in a Cartesian coordinate system represent negative x-values, which means they have potential for a log x transformation.

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  • 8. 

    Which quadrants have potential for a log y transformation

    • A.

      Quadrant 1.

    • B.

      Quadrant 2

    • C.

      Quadrant 3

    • D.

      Quadrant 4

    Correct Answer(s)
    C. Quadrant 3
    D. Quadrant 4
    Explanation
    A log y transformation is used when the data is skewed or when the range of values is very large. In Quadrant 3 and Quadrant 4, the y-values are negative or close to zero, which can result in a skewed distribution or a wide range of values. Therefore, these quadrants have the potential for a log y transformation to normalize the data and make it more suitable for analysis.

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  • 9. 

    The residual plot above shows the original data is potentially from which quadrants

    • A.

      Quadrant 1

    • B.

      Quadrant 2

    • C.

      Quadrant 3

    • D.

      Quadrant 4

    Correct Answer(s)
    A. Quadrant 1
    B. Quadrant 2
    Explanation
    The residual plot above suggests that the original data is potentially from Quadrant 1 and Quadrant 2. This is because the residuals, which are the differences between the observed and predicted values, are positive in Quadrant 1 and negative in Quadrant 2. This indicates that the model tends to overestimate the values in Quadrant 1 and underestimate the values in Quadrant 2. Therefore, the original data is likely to be located in these two quadrants.

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  • 10. 

    The residual plot above shows the original data is potentially from which quadrants

    • A.

      Quadrant 1

    • B.

      Quadrant 2

    • C.

      Quadrant 3

    • D.

      Quadrant 4

    Correct Answer(s)
    C. Quadrant 3
    D. Quadrant 4
    Explanation
    The residual plot above shows that the residuals, or the differences between the observed and predicted values, are predominantly negative in Quadrant 3 and positive in Quadrant 4. This indicates that the original data points are potentially located in these quadrants.

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  • 11. 

    The residual plot above shows the original data can potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It can't be linearised with a log transformation

    Correct Answer(s)
    A. Log x transformation
    B. Log y transformation
    Explanation
    The residual plot above suggests that the original data can potentially be linearized with a log x transformation and a log y transformation. This means that taking the logarithm of the x-values and the y-values may help to create a linear relationship between the variables.

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  • 12. 

    The residual plot above shows the original data can potentially be linearised with :

    • A.

      Log x transformation

    • B.

      Log y transformation

    • C.

      It can't be linearised with a log transformation

    Correct Answer
    C. It can't be linearised with a log transformation
    Explanation
    The residual plot above indicates that the original data cannot be linearized with a log transformation. This means that neither a log x transformation nor a log y transformation can be used to make the data fit a linear model. The residuals are not randomly scattered around zero, suggesting that there is some non-linear relationship between the variables. Therefore, a log transformation is not suitable for linearizing the data in this case.

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  • 13.