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user137795
user137795

deletedDeleted, see quesionquestion comment for content. (This post leftremains here because I can't delete an accepted answer, see https://meta.stackexchange.com/questions/14932/allow-author-of-accepted-answer-to-delete-it-in-certain-circumstances).

deleted, see quesion comment for content. (This post left because I can't delete an accepted answer)

Deleted, see question comment for content. (This post remains here because I can't delete an accepted answer, see https://meta.stackexchange.com/questions/14932/allow-author-of-accepted-answer-to-delete-it-in-certain-circumstances).

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user137795
user137795

Assuming the real model is: $$ y_i = \beta_0 + \beta_1 X_{i1} + \epsilon_i $$ but you add a factor $X_{2i}$ which not relate the $y_i$ to model and fit the new model $$ y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \epsilon_i $$ In general, you will get a $\hat{\beta_2} \neq 0$, then if you run the model to predict something including factor $X_{i2}$deleted, you will suffer over-fitsee quesion comment for content. (This post left because I can't delete an accepted answer)

Assuming the real model is: $$ y_i = \beta_0 + \beta_1 X_{i1} + \epsilon_i $$ but you add a factor $X_{2i}$ which not relate the $y_i$ to model and fit the new model $$ y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \epsilon_i $$ In general, you will get a $\hat{\beta_2} \neq 0$, then if you run the model to predict something including factor $X_{i2}$, you will suffer over-fit.

deleted, see quesion comment for content. (This post left because I can't delete an accepted answer)

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user137795
user137795

Assuming the real model is: $$ y_i = \beta_0 + \beta_1 X_{i1} + \epsilon_i $$ but you add a factor $X_{2i}$ which not relate the $y_i$ to model and fit the new model $$ y_i = \beta_0 + \beta_1 X_{i1} + \beta_2 X_{i2} + \epsilon_i $$ In general, you will get a $\hat{\beta_2} \neq 0$, then if you run the model to predict something including factor $X_{i2}$, you will suffer over-fit.