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Grammar, clarity, tweak notation (e.g. the index in yi isn't needed since it's talking about a single prediction anyways)
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Given a data set of 100n=100 observations, (n=100) withk=50 independent variables xi, and one dependent variable (y) and 50 independent variables (k=50). Inference, inference answers the following two questions such as:

  1. WhichWhat subset of or combination of the 50k independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase? (i.e. yx1)

Both of these questions are questions about the parameters in the “true model” that generated the data.

 

Prediction answers a much simpler question:

  1. Given new values for eachIf we set the independent variablevariables xi to some specific values, what'swhat is my best guess offor y?

The lastThis question does not ask anything about the parameters in the true model. Nor does it necessarily appeal torequire the existence of a “true model”. SimplyPrediction simply involves a plug-and-chug that generatesto generate a value ^yiˆy that is ideally close to yiy.

Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase?

Both of these questions are questions about the parameters in the “true model” that generated the data.

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

The last question does not ask anything about the parameters in the true model. Nor does it necessarily appeal to the existence of a “true model”. Simply a plug-and-chug that generates a value ^yi that is ideally close to yi.

Given a data set of n=100 observations, k=50 independent variables xi, and one dependent variable y, inference answers questions such as:

  1. What subset or combination of the k independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase? (i.e. yx1)

Both of these questions are questions about the parameters in the “true model” that generated the data.

 

Prediction answers a much simpler question:

  1. If we set the independent variables xi to some specific values, what is my best guess for y?

This question does not ask anything about the parameters in the true model. Nor does it require the existence of a “true model”. Prediction simply involves a plug-and-chug to generate a value ˆy that is ideally close to y.

Added frequentist flavor.
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Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase?

Both of these questions are questions about the parameters in the “true model” that generated the data.

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

The last question does not ask anything about the parameters in the true model. Nor does it necessarily appeal to the existence of a “true model”. Simply a plug-and-chug that generates a value ^yi that is ideally close to yi.

Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase?

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase?

Both of these questions are questions about the parameters in the “true model” that generated the data.

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

The last question does not ask anything about the parameters in the true model. Nor does it necessarily appeal to the existence of a “true model”. Simply a plug-and-chug that generates a value ^yi that is ideally close to yi.

Removed budget example
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Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If my company gave me $25,000I were able to maximize sum(y)increase the value of x1 by 10%, which observations and independent variableshow much would I seek to changey increase?

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If my company gave me $25,000 to maximize sum(y), which observations and independent variables would I seek to change?

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?

Given a data set of 100 observations (n=100) with one dependent variable (y) and 50 independent variables (k=50). Inference answers the following two questions:

  1. Which subset of or combination of the 50 independent variables affect y?
  2. If I were able to increase the value of x1 by 10%, how much would y increase?

Prediction answers a much simpler question:

  1. Given new values for each independent variable, what's my best guess of y?
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