Why did we not extend the red line (for the women) all the way to 74 inches, instead of stopping at 69 inches? Choose the correct answer below.

Question

Why did we not extend the red line (for the women) all the way to 74  inches, instead of stopping at 69  inches? Choose the correct answer below.

BlackTom AI · Accepted Answer

The question asks why the red line for women was not extended to 74 inches and instead stops at 69 inches. Each option should be evaluated for accuracy and reasoning quality.
Option 1: 'There are no women taller than 69 inches, so the line should stop at 69 inches to avoid extrapolating.' This statement aligns with a cautious data-interpretation principle: if the dataset contains no observations beyond 69 inches, extending the line to 74 would require extrapolation beyond the available data, which can be misleading. Keeping the line at 69 inches respects the data boundary and avoids unsupported conclusions.
Option 2: 'It is incorrect that the line stops at 69 inches. The line should have extended to 74 inches.' This contradicts standard data-visualization practice: extending beyond observed data without evidence constitutes extrapolation. Unless there is a justified model or underlying data to support such extension, this option is incorrect because it assumes information not present in the data.
Option 3: 'Not many women have a shoe size bigger than size 9, and the height of 69 inches corresponds with that data point, so the line should stop at size 9 to avoid extrapolating.' This option confuses variables (shoe size vs. height) and makes an inconsistent claim about a height corresponding to a shoe size. It also incorrectly frames the stopping point as tied to a shoe-size data point, which is not the stated reason for stopping at 69 inches. Therefore, this reasoning is misleading and incorrect.
Option 4: 'The line for the men starts about halfway up the women's line so the women's line stops about halfway up the men's line in order to avoid too much overlap on the scatterplot.' This introduces a formatting/visual overlap concern as the primary reason, rather than the actual data boundary. If the question emphasizes avoiding extrapolation due to lack of data above 69 inches, this option misattributes the stopping point to overlap considerations rather than data-supported limits, making it incorrect.
In summary, Option 1 correctly cites the absence of data beyond 69 inches and the practice of avoiding extrapolation, while Options 2, 3, and 4 misinterpret the reason, rely on extrapolation or unrelated factors, or mix up variables. The justification that the line should stop at 69 inches to avoid extrapolating is the appropriate, data-driven rationale.

251A-STATS-10-LEC-1 Quiz #5- Requires Respondus LockDown Browser

Why did we not extend the red line (for the women) all the way to 74 inches, instead of stopping at 69 inches? Choose the correct answer below.

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251A-STATS-10-LEC-1 Quiz #5- Requires Respondus LockDown Browser

Why did we not extend the red line (for the women) all the way to 74 inches, instead of stopping at 69 inches? Choose the correct answer below.

查看解析

登录即可查看完整答案

类似问题

Suppose a one-year-old child has a shoulder girth of 56 cm. Predicting the height of this child would require extrapolation. The data used to create the model is for people with approximately 90 to 130 cm shoulder girth. The linear model may no longer hold outside the range of the data.

We say we have ____________________ when a regression equation is used to make a prediction for a value of x that is outside the range of the values of x that were used to construct the regression equation.

Would we use the regression line to predict growth in per capita income for cities where 70% of residents have at least 4 years of college?

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Consider the estimated regression model Y_hat = 0.5 + 1.2X1. This model was estimated on a data set where X1 has a range of values between 8 and 34. Should we use the model to predict Y_hat=2.9 = 0.5 + 1.22 for X1=2?