Question at position 22 How is the residual calculated in a linear regression model?By multiplying the regression coefficient with the predictor variableBy subtracting the predicted value of the dependent variable from its actual valueBy adding the intercept and the product of the slope and the predictor variableBy observing the error.BlackTom题目解析

Question

BlackTom AI · Accepted Answer

To begin, let's lay out what a residual is in linear regression and how it is defined in common notation. The residual for an observation is the difference between the observed value of the dependent variable and the value predicted by the regression model.
Option 1: 'By multiplying the regression coefficient with the predictor variable' — This describes the component used to compute a predicted value (the slope times the predictor), not the residual itself. It does not account for the actual observed outcome, so it cannot be the residual.
Option 2: 'By subtracting the predicted value of the dependent variable from its actual value' — This matches the standard residual formula: residual = y − ŷ, where y is the actual value and ŷ is the predicted value. It directly expresses the difference between observation and model prediction.
Option 3: 'By adding the intercept and the product of the slope and the predictor variable' — This is the calculation of the predicted value ŷ (the regression line), not the residual. It lacks the actual observed value and thus does not yield the residual.
Option 4: 'By observing the error.' — This is vague and informal. While residuals are the errors of prediction, saying 'observing the error' without the explicit formula y − ŷ fails to define the residual precisely and can be misleading in a mathematical context.
In summary, only Option 2 directly expresses the precise residual definition as the difference between the observed outcome and its predicted value, aligning with the standard residual concept in linear regression.

查看解析

登录即可查看完整答案

类似问题

Question at position 4 The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.constant termresidualerror termmodel parameterClear my selection

A regression model made a prediction that a particular participant should have a value of 17. However, the actual data point instead has a value of 10. What term refers to the difference between the predicted value and the actual value?

What is the name of the distance captured by the purple dotted line (shown below)?

If our model says this: Salary = B1 + B2*Hits + e And B1 = 10 and B2 = 3. What is the e for a player who has 9 hits and a salary of 57?

In the equation _{Savings=\beta_0+\beta_1Income+\mu}. What is the residual for the 10th observation if \hat{savings}=$400 and savings=$1000?

Refer to Scenario 8-13. d) The actual girls’ FSL high jump champion in 2014 was Naomi Jimenez from Westtown School, who jumped 62 inches that day. Calculate her residual.

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