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A linear regression was conducted on the number of cigarettes a person smokes in a day versus the number of times they cough in a day. Suppose the number of cigarettes a person smokes in a day is our x variable and the number of times they cough in a day is the y variable.

In linear regression, the y variable is referred to as the:

a) response variable.
b) correlation coefficient.
c) explanatory variable.
d) true variable.

User JFerro
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2 Answers

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In linear regression, the framework typically involves a relationship between two types of variables: the independent variable and the dependent variable. The independent variable, also known as the predictor or explanatory variable, is the one that you manipulate or observe changes in to see how it affects the dependent variable. The dependent variable is the one you're particularly interested in; it is thought to depend on or be a consequence of the changes in the independent variable.

Now, let's apply this framework to your context. You have mentioned that the number of cigarettes a person smokes in a day (let's call this X) is plotted against the number of times they cough in a day (let's call this Y). In this scenario, X is your independent variable because it's the factor you're considering as the possible influence. You're seeing how changes in X (cigarette consumption) affect Y (frequency of coughing).

The variable Y, being the outcome that you're interested in and the one that's thought to be influenced by X, is termed the dependent variable in a broad statistical sense. In the context of linear regression specifically, the dependent variable is more commonly known as the "response variable." The term "response" references the idea that this variable is "responding" to changes in the independent (or explanatory) variable.

Therefore, referring back to your question, the number of times they cough in a day (Y variable) in the context of a linear regression is referred to as the:

a) response variable.

This is the correct term since it's the variable that we are trying to predict or explain changes in, using the independent variable which, in this case, is the number of cigarettes smoked in a day.

User Kyle Heuton
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Answer:

a) response variable

Explanation:

The response variable is the variable that depends on other variables such as the independent or explanatory variable, it is the variable that is being tested. The response variable is also called the dependent variable.

In linear regression, the y variable is referred to as the response variable while the x variable is referred to as the explanatory or independent variable.

In this case the y variable is "the number of times they cough in a day" and this variation depends on the x variable "number of cigarettes a person smokes in a day".

User Dastrobu
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