In the following regression equation, y is a binary variable:

y=β0+β1x1+...+βkxk+u

Notice that P(y=1|x)=E(y|x) where P(X) stands for probability of event X occurring
So, P(y=1|x)=
ˆ
β
0+
ˆ
β
x1+...+
ˆ
β
xk

In this case, the estimated slope coefficient
^
β1
measures _____.

Question

In the following regression equation, y is a binary variable:

y=β0+β1x1+...+βkxk+u

Notice that P(y=1|x)=E(y|x) where P(X) stands for probability of event X occurring
So, P(y=1|x)=
ˆ
β
0+
ˆ
β
x1+...+
ˆ
β
xk

In this case, the estimated slope coefficient 
^
β1
 measures _____.

BlackTom AI · Accepted Answer

The model given is a linear probability model where the dependent variable y is binary (0 or 1) and the expectation E(y|x) is interpreted as the predicted probability P(y=1|x). In this setup, the coefficient on x1, denoted β1 hat, represents the average change in the predicted probability of the event y=1 associated with a one-unit increase in x1, holding all other regressors constant. This interpretation comes directly from the linear form y = β0 + β1 x1 + ... + βk xk + u, where the partial derivative of E(y|x) with respect to x1 is ∂E(y|x)/∂x1 = β1.

Therefore, the statement that the estimated slope coefficient β1 hat measures the predicted change in the probability of success (y=1) when x1 increases by one unit, everything else remaining constant, is the correct interpretation in the context of a linear probability model.

Note: In practice, the linear probability model can produce predicted probabilities outside the [0,1] interval and standard errors can be biased due to heteroskedasticity. In contrast, nonlinear models like logit or probit interpret coefficients differently (as changes in the latent utility or as marginal effects at certain values of x), which is why those contexts require different interpretations. However, within this regression specification, the described interpretation for β1 holds true.

AS.440.606.80.SP25 M07: Assignment

In the following regression equation, y is a binary variable: y=β0+β1x1+...+βkxk+u Notice that P(y=1|x)=E(y|x) where P(X) stands for probability of event X occurring So, P(y=1|x)= ˆ β 0+ ˆ β x1+...+ ˆ β xk In this case, the estimated slope coefficient ^ β1 measures _____.

查看解析

登录即可查看完整答案

类似问题

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

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