Consider the estimated regression model Y_hat = 0.5 + 1.2*X1. 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 + 1.2*2 for X1=2?

Question

Consider the estimated regression model Y_hat = 0.5 + 1.2*X1. 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 + 1.2*2   for X1=2?

BlackTom AI · Accepted Answer

Question restatement: The estimated regression model is Y_hat = 0.5 + 1.2*X1, estimated on data where X1 ranges from 8 to 34. The question asks whether we should use the model to predict Y_hat = 2.9 for X1 = 2, given the formula Y_hat = 0.5 + 1.2*2.

Option 1: True. Why this is not correct: The model was trained with X1 values only between 8 and 34, so predicting at X1 = 2 would be an extrapolation outside the observed data range. Predictions outside the training domain are unreliable because the relationship estimated may not hold beyond the range of X1 used to fit the model. Also, the stated calculation Y_hat = 2.9 using X1 = 2 ignores the warning about extrapolation and uses a value not supported by the data range.

Option 2: False. Why this is correct: It is inappropriate to use the model to predict at X1 = 2 since 2 lies well below the observed range (8 to 34). Predictions outside the training interval are prone to large errors and lack empirical justification. Even though the algebraic substitution yields Y_hat = 0.5 + 1.2*2 = 2.9, this predicted value is not trustworthy because it corresponds to an X1 value outside the domain where the model was estimated, so the model should not be used to make that prediction.

Additional clarifications to avoid a common pitfall: It is tempting to compute the numerical prediction as if the algebra were the only criterion, but the key methodological rule is about the data domain. The conclusion hinges on the domain of X1, not on the arithmetic of the equation itself. Since the question explicitly mentions the training range, the correct stance is to reject predictions at X1 = 2 as inappropriate.

2025WI_MSDS_410-DL_SEC56 Quiz #1: OLS Regression Basics

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?

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.

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.

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?

A graph showing new job growth by month from September 2010 to December 2010 shows a steady increase. A popular news magazine makes the claim that the job outlook is great for the New Year and beyond. This is an example of a(n):

Find the absolute (global) maximum \( y \) value of the function:\( f(x)=2x^3+0x^2+-24x+5 \)On the interval \( [-9, 10] \)

Find the absolute (global) maximum [math: y] value of the function:[math: f(x)=2x3+0x2+−24x+5]On the interval [math: [−9,10]]

Two numbers [math: a]nd [math: b] sum to make 30.Find the maximum value of their product (multiplied together), [math: P].Show your answer correct to 2 decimal places.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单