(Continued from the previous question).（接上一个问题）。 A person of height 179 cm weighs 82 kg. If the regression equation is used to predict身高179厘米的人体重82公斤。如果使用回归方程来预测their weight, then the residual will be closest to:它们的重量，则残差将最接近：

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Question restatement: The prompt asks, 'If the regression equation is used to predict their weight, then the residual will be closest to: [in Chinese: 使用回归方程来预测他们的体重，则残差将最接近：]' and provides an example data point: a person 179 cm tall weighs 82 kg. It is a continuation from a previous question.

Key issue: The answer options are missing in the provided data. There is an explicit reference to an option 'c. 8 kg / 8公斤', but no list of all answer choices is present. Without the full set of options, we cannot determine which residuals were being proposed as candidates, nor can we assess which is closest.

What a residual is: In regression, the residual for an observation is calculated as the observed value minus the predicted value: Residual = Observed weight − Predicted weight. Here, Observed weight = 82 kg. To know the residual, we would need the predicted weight from the regression equation for height 179 cm.

What’s needed to compute the residual:
- The regression equation (for weight as the dependent variable and height as the predictor). This typically has the form: Predicted weight = a + b × (height in cm).
- The intercept (a) and slope (b) coefficients from fitting the regression to the relevant data set.
- Plug height = 179 into the equation to obtain Predicted weight, then subtract from 82 kg to get the residual.

If the regression equation happened to predict 74 kg for 179 cm, the residual would be 82 − 74 = 8 kg. If it predicted something else, the residual would be that difference, possibly negative if the predicted weight exceeded 82 kg.

But with missing options, we cannot evaluate which residual value is listed as closest, nor confirm whether 8 kg (the cited option) is correct in this context.

Guidance for solving when you have the regression equation and options:
- Compute Predicted weight at height 179 cm using the regression equation.
- Subtract: Residual = 82 − Predicted weight.
- Compare the resulting residual to each option and pick the one with the smallest magnitude (absolute value).

Caveat: If the problem’s options include positive and negative residuals, remember to compare absolute values to determine which residual is closest in magnitude.

In summary, due to the missing list of answer choices, it’s not possible to determine which residual is closest from the provided data. Once the full set of options is available, apply the steps above to identify the correct residual with respect to the regression equation.

MUF0142 Fund. Mathematics Unit 2 - Semester 2, 2025 MUF0142 基金。数学第 2 单元 - 第 2 学期，2025 6.5 Regression Quiz (Formative) 6.5 回归测验（形成性）

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