When attempting to communicate how much one variable changes on average as a function of the other, which of the following measures is most appropriate?

Question

BlackTom AI · Accepted Answer

Here we examine what each measure tells us about the relationship between two variables.
Option 1: Simple Linear Regression Coefficient. This coefficient represents the slope of the regression line, i.e., the average change in the dependent variable for a one-unit change in the independent variable. It directly communicates how much one variable changes on average as the other varies, which matches the question's goal.
Option 2: Correlation Coefficient. This statistic describes the strength and direction of a linear association between two variables, but it is unitless and standardized. It does not quantify the actual amount of change in one variable per unit change in the other, so it does not answer the question about average change magnitude.
Option 3: Covariance. Covariance measures the joint variability of the two variables and reflects direction of association, but its scale depends on the variables' units. It does not provide a standardized rate of change, making it less informative for stating how much one variable changes on average with respect to the other.
In sum, the slope from a simple linear regression captures the requested notion of average change per unit change, whereas correlation describes strength and direction in a standardized way and covariance describes joint variability without conveying a unit-specific rate of change.

When attempting to communicate how much one variable changes on average as a function of the other, which of the following measures is most appropriate?单项选择题

类似问题

The beta coefficient in a multiple regression equation indicates:

On March 12, we did a warm-up exercise. What is the estimate for \(\beta_1\)?

Which of the following trees corresponds to a potential parse of the ambiguous sentence below, with correct syntactic categories? Some diagnostics are provided.

Which of the following sentences contain two non-finite verbs? Select all that apply.

Analyze the following sentence: The sentence contains [ Select ] 8 6 5 7 3 4 functional words, [ Select ] 2 3 1 4 5 count nouns, [ Select ] 4 5 2 1 3 mass nouns, and [ Select ] 1 5 2 3 4 adjectives.

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