Which of the following are the assumptions of regression analysis? The relationship between y and x is linear. The errors all have the same variance. The errors are independent of each other. The errors are all normally distributed.[Fill in the blank]单项选择题
A
a. i, ii and iii
B
b. i, ii and iv
C
c. ii, iii and iv
D
d. i, ii, iii and iv

Question

Which of the following are the assumptions of regression analysis? The relationship between y and x is linear. The errors all have the same variance. The errors are independent of each other. The errors are all normally distributed.[Fill in the blank]单项选择题

A

a. i, ii and iii

B

b. i, ii and iv

C

c. ii, iii and iv

D

d. i, ii, iii and iv

BlackTom AI · Accepted Answer

To analyze the question, I will go through each statement and examine whether it is considered an assumption in regression analysis.

Option a: i, ii and iii. This choice includes linearity, constant variance, and independence, but it excludes normality of the errors. While linearity, homoscedasticity (constant variance), and independence are standard assumptions for estimation, normality of the errors is often required for valid inference (e.g., confidence intervals, hypothesis tests) in small samples. Omitting normality means this option is incomplete if the context requires inference.

Option b: i, ii and iv. This set contains linearity, constant variance, and normality, but it leaves out the independence of errors. Independence is a key assumption to ensure that error terms are not correlated across observations; ignoring it leads to biased standard errors and unreliable inferences. Therefore, this option is missing a crucial assumption.

Option c: ii, iii and iv. Here, the constants variance, independence, and normality are listed, but linearity is not included. Without a linear relationship between y and x, the regression model would not be appropriate or interpretable in the standard linear-regression sense, so this option is also flawed.

Option d: i, ii, iii and iv. This option includes all four statements: (i) the relationship between y and x is linear, (ii) the errors have constant variance (homoscedasticity), (iii) the errors are independent of each other, and (iv) the errors are normally distributed. In many regression frameworks, especially for classical linear regression, these four conditions cover both the estimation properties (linearity, homoscedasticity, independence) and the inference properties (normality of errors for reliable small-sample tests). Although some texts emphasize that normality is not necessary for unbiased coefficient estimation, it is commonly listed as part of the regression assumptions when inference is concerned.

Therefore, comparing all options, the most comprehensive and commonly accepted set that includes all standard assumptions is option d. A careful reader should recognize that the inclusion of normality (iv) strengthens the validity of inferential procedures, even if estimation can proceed under non-normal errors with large samples. The other options each omit at least one essential assumption, which is why they are not preferred as the complete set of regression assumptions.

Which of the following are the assumptions of regression analysis? The relationship between y and x is linear. The errors all have the same variance. The errors are independent of each other. The errors are all normally distributed.[Fill in the blank]单项选择题

类似问题

what is the major assumption I asked in class when I discussed the statistical properties of regression coefficients?

Which of these is NOT an assumption of Linear Regression?

Which of the following assumptions do we need to check to make sure our regression is appropriate?

In a multiple regression model, the error term e is assumed to be a random variable with a mean of

Consider the following multiple linear regression (MLR) model, y = β0 + β1x1 + …+ βkxk + u. Which of the following statements is correct?

Refer to Ch3 and Ch4. Consider the following multiple regression model: y = β0 + β1x1 + …+ βkxk + u. Which of the following statements is correct? Note: this question is about assumptions MLR.1 through MLR.6 (which are called the classical linear model (CLM) assumptions).

Question at position 8 An excess of growth hormone (GH) before puberty can result in the development ofgigantism.Graves' disease.acromegaly.pituitary dwarfism.Clear my selection

Question at position 6 The most abundant supporting cells in the central nervous system are called Question Blank 1 of 1[input].

更多留学生实用工具

智能学习助手

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