散点图、模型残差与预测
SAT 知识点 15 3:44 英语旁白 · 英中内嵌字幕
章节
文本转录
A residual is observed minus predicted output.
残差等于观测值减去预测值。
A journey model T equals 5 plus 2 d uses minutes for T and kilometres for d.
行程模型 T = 5 + 2d 中，T 的单位为分钟，d 的单位为公里。
T of 4 equals 5 min plus 2 min per km times 4 km, which equals 13 min.
当 d = 4 时，T(4) = 5 min + (2 min/km)(4 km) = 13 min。
For observed time 16 min, e equals T sub obs minus T sub pred, which equals 16 min minus 13 min, which equals 3 min.
若观测时间为 16 min，则 e = T_obs - T_pred = 16 min - 13 min = 3 min。
Each task gives its own data.
每个任务都有其专属数据。
Do not copy the worked example’s numbers.
请勿照搬示例中的数值。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
请利用前几页的完整背景信息。
The intercept predicts 8 minutes at zero distance; zero lies outside the observed range, so this interpretation is an extrapolation.
截距预测距离为零时用时八分钟；但零不在观测范围之内，所以这种解释是外推。
The slope predicts an extra 1.5 minutes per kilometre.
斜率预测每多一公里多用一点五分钟。
T of 6 is 8 minutes plus 1.5 minutes per kilometre times 6 kilometres, which is 17 minutes.
T(6) 等于八分钟加每公里一点五分钟乘六公里，即十七分钟。
The residual is 15 minus 17, which is negative 2 minutes, below the line.
残差等于十五减十七，即负二分钟，点在直线下方。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
使用前面页面的完整背景信息。
Seven is inside 2–10, so interpolation.
七在二到十之间，所以是内插。
Twenty is outside, so extrapolation with weaker support.
二十在范围之外，所以是外推，依据更弱。
Traffic, loading and other conditions can influence time; a fitted association does not isolate their effects.
交通、装货和其他条件都会影响用时；拟合出的关联并不能把它们各自的影响分离出来。
Pause here and attempt the task before revealing the reasoning.
请先暂停，完成这道原创练习再继续。
Use the full context on the preceding pages.
使用前面页面的完整背景信息。
The ratios are all 3, while the differences vary.
相邻两项的比都是三，而差各不相同。
The exponential rule is y equals 6 times 3 to the x.
指数规律是 y 等于六乘三的 x 次方。
Under continued growth by a factor of three, y of 4 is 6 times 3 to the fourth, which is 486.
如果继续按三倍增长，y(4) 等于六乘三的四次方，即四百八十六。
This is a model-based extrapolation, not a guaranteed next observation.
这是基于模型的外推，而不是对下一个观测值的保证。
Return to the task and explain why the method fits.
回到该任务，并解释为何此方法适用。
Original practice does not predict an official score.
原始练习无法预测官方分数。
Complete required live or recorded evidence separately.
请单独完成所需的现场或录制证据。
Pause and test yourself. Cover the worked answer, rebuild the answer to the last example in your own words, and name one condition that would change it before you check.
暂停一下，自我检测：遮住示范答案，用自己的话重做最后一个例子的答案，并在核对之前说出一个会改变结论的条件。