2616 Scatter Plot Transformations Reciprocals

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| By Anthony Nunan
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Anthony Nunan
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2616 Scatter Plot Transformations Reciprocals - Quiz

1/x (or reciprocal x) and 1/y (or reciprocal y) transformations


Questions and Answers
  • 1. 

    The 1/y (or reciprocal y) transformation linearises the scatter plot by :

    • A.

      Turning the y values into 1/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 1/y values
    B. Compressing the y axis values
    D. Leaving the x axis values the same
    Explanation
    The 1/y transformation linearizes the scatter plot by turning the y values into 1/y values. This means that as the y values increase, their corresponding 1/y values decrease, creating a more linear relationship. Additionally, the transformation compresses the y-axis values, making the data points spread out more evenly along the axis. However, the x-axis values remain the same, as the transformation only affects the y values.

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  • 2. 

    The 1/x transformation linearises the scatter plot by :

    • A.

      Changing the x values to 1/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 1/x values
    B. Compressing the x axis values
    D. Leaving the y values as they are
    Explanation
    The 1/x transformation linearizes the scatter plot by changing the x values to 1/x values. This transformation inversely scales the x-axis, compressing the values. As a result, the scatter plot becomes more evenly spread out along the x-axis. The y values remain unchanged, meaning they are not affected by this transformation.

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  • 3. 

    The scatter plot above will potentially be linearised with :

    • A.

      1/x transformation

    • B.

      1/y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer
    A. 1/x transformation
    Explanation
    The scatter plot above will potentially be linearized with a 1/x transformation. This transformation involves taking the reciprocal of the x-values, which can help to spread out the data points and make the relationship between the variables more linear. By applying this transformation, the relationship between the variables may become more apparent and easier to analyze.

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  • 4. 

    The scatter plot above will potentially be linearised with :

    • A.

      1/x transformation

    • B.

      1/y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer(s)
    A. 1/x transformation
    B. 1/y transformation
    Explanation
    The scatter plot can potentially be linearized with the 1/x transformation and the 1/y transformation. These transformations can help to straighten out the relationship between the variables and make it more linear. However, if the scatter plot is in the wrong quadrant for these transformations, they may not be effective in linearizing the data.

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  • 5. 

    The scatter plot above will potentially be linearised with :

    • A.

      1/x transformation

    • B.

      1/y transformation

    • C.

      It is is the wrong quadrant for these transformations

    Correct Answer
    B. 1/y transformation
    Explanation
    The scatter plot can potentially be linearized with a 1/y transformation. This means that by taking the reciprocal of the y-values, the relationship between the variables may become linear. This transformation is useful when the relationship between the variables is non-linear and the y-values are spread out across a wide range. By applying the 1/y transformation, the data points may become more closely clustered and form a linear pattern.

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  • 6. 

    The scatter plot above will potentially be linearised with :

    • A.

      1/x transformation

    • B.

      1/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 the 1/x and 1/y transformations to potentially linearize it. In the wrong quadrant, these transformations would not be effective in straightening out the relationship between the variables.

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  • 7. 

    Which quadrants have potential for a 1/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 1/x transformation involves taking the reciprocal of a number. In this case, potential for a 1/x transformation exists in Quadrant 2 and Quadrant 3. In Quadrant 2, the x-values are positive and the y-values are negative, while in Quadrant 3, both x and y values are negative. Taking the reciprocal of these numbers will result in positive values. In Quadrant 1, the x and y values are both positive, so taking the reciprocal will still result in positive values. In Quadrant 4, the x-values are negative and the y-values are positive, so taking the reciprocal will result in negative values.

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  • 8. 

    Which quadrants have potential for a 1/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 1/y transformation involves taking the reciprocal of the y-coordinate of a point. In Quadrant 3 and Quadrant 4, the y-coordinates of points are negative. Therefore, when we take the reciprocal of a negative number, it becomes positive. Hence, Quadrant 3 and Quadrant 4 have the potential for a 1/y transformation.

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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 shows that the original data is potentially from Quadrant 1 and Quadrant 2. This can be inferred from the fact that the residuals (the vertical distances between the observed data points and the regression line) are positive in Quadrant 1 and negative in Quadrant 2. This suggests that the observed data points are generally above the regression line in Quadrant 1 and below the regression line in Quadrant 2, indicating a positive relationship between the variables being analyzed.

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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 original data is potentially from Quadrant 3 and Quadrant 4. This is because the residuals, which represent the difference between the observed values and the predicted values, are mostly negative in Quadrant 3 and mostly positive in Quadrant 4. This suggests that the model tends to underestimate the values in Quadrant 3 and overestimate the values in Quadrant 4.

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  • 11. 

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

    • A.

      1/x transformation

    • B.

      1/y transformation

    • C.

      It can't be linearised with a reciprocal transformation

    Correct Answer(s)
    A. 1/x transformation
    B. 1/y transformation
    Explanation
    The residual plot above indicates that the original data may have a non-linear relationship. The 1/x transformation and 1/y transformation are both potential methods to linearize the data. By taking the reciprocal of either the independent variable or the dependent variable, the relationship between the variables may become linear. However, it is not possible to linearize the data with a reciprocal transformation alone. Therefore, both the 1/x transformation and the 1/y transformation are viable options for linearizing the data.

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  • 12. 

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

    • A.

      1/x transformation

    • B.

      1/y transformation

    • C.

      It can't be linearised with a reciprocal transformation

    Correct Answer
    C. It can't be linearised with a reciprocal transformation
    Explanation
    The residual plot above indicates that the relationship between the original data and the predicted values cannot be linearized by using a reciprocal transformation. This means that taking the reciprocal of either the x or y values will not result in a linear relationship. Therefore, the correct answer is that the data cannot be linearized with a reciprocal transformation.

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  • 13.