2614 Scatter Plot Transformations Logs
Log x and log y transformations
- 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 sameExplanation
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.Rate this question:
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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 areExplanation
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.Rate this question:
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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 transformationExplanation
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.Rate this question:
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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 transformationExplanation
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.Rate this question:
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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 transformationExplanation
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.Rate this question:
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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 transformationsExplanation
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.Rate this question:
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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 3Explanation
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.Rate this question:
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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 4Explanation
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.Rate this question:
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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 2Explanation
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.Rate this question:
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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 4Explanation
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.Rate this question:
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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 transformationExplanation
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.Rate this question:
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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 transformationExplanation
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.Rate this question:
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- 13.
