Cross Validated Asked by Chochot on January 5, 2022

I have a set of observed values ($y_{1Obs}$) and 3 predictive variables (n = 27). I use multiple linear regression to create a linear model:

$Z_1=alpha_0 + alpha_1 W_1 + alpha_2 X_1 + alpha_3 Y_1$

Where $Z_1$ is my response variable, $alpha_0$ is the intercept, $alpha_1 , alpha_2 , alpha_3$ are regression coefficients and $W_1, X_1, Y_1$ are predictive variables.

I also have a second set of observed values ($y_{2Obs}$) and 3 different predictive variables (n = 27). I again use multiple linear regression to create a second linear model of the same form:

$Z_2=beta_0 + beta_1 W_2 + beta_2 X_2 + beta_3 Y_2$

Where $Z_2$ is my response variable, $beta_0$ is the intercept, $beta_1 , beta_2 , beta_3$ are regression coefficients and $W_2, X_2, Y_2$ are predictive variables.

With 27 predicted values from each model I then calculate the predicted change between the two:

$Delta Z_{Pred}=Z_2 – Z_1$

While my observed change comes from the two sets of observed values used to create the two linear models:

$Delta Z_{Obs}=y_{2Obs} – y_{1Obs}$

**My question is:** what formula do I use to calculate the RMSE of my predictions ($Delta Z_{Pred}$) that will propagate the errors from predictions of $Z_1$ and $Z_2$?

I’ve tried using the following formula though I’m not convinced this is correct:

$RMSE_{Delta Z_{Pred}} = sqrt{{RMSE_1}^2 + {RMSE_2}^2}$

Where $RMSE_1$ and $RMSE_2$ are the RMSEs from the first two models shown above.

Not a complete answer but a couple of hopefully useful comments:

- The formula $RMSE_{Delta Z_{Pred}} = sqrt{{RMSE_1}^2 + {RMSE_2}^2}$ may work for independent sets of responses and predictors, but is likely to be false if the two sets are correlated. For example, if your two sets of predictors and responses are the same $RMSE_{Delta Z_{Pred}}=0$, while $sqrt{{RMSE_1}^2 + {RMSE_2}^2} > 0$.
- If you are interested in $Delta Z_{Pred}$, I suggest regressing it on the six predictors - although this is not what you are asking, it might server your goal.

Answered by Pere on January 5, 2022

1 Asked on January 14, 2021 by doxav

multiarmed bandit optimization queueing real time time series

1 Asked on January 14, 2021

1 Asked on January 14, 2021 by user261225

1 Asked on January 13, 2021 by katy

0 Asked on January 13, 2021

2 Asked on January 13, 2021 by crazydriver

1 Asked on January 13, 2021 by vin

bayesian bayesian network conditional probability inference posterior

0 Asked on January 12, 2021 by g-s-luimstra

convolution filter gradient descent neural networks optimization

1 Asked on January 12, 2021 by somethingsomething

1 Asked on January 12, 2021 by user3136

1 Asked on January 11, 2021 by ad-van-der-ven

bernoulli distribution distributions exponential distribution probability

0 Asked on January 11, 2021 by jonas-palaionis

0 Asked on January 11, 2021 by sventon

2 Asked on January 11, 2021 by benjamin-phua

1 Asked on January 10, 2021 by confusedmathstudent

conditional expectation conditional probability expected value frequency severity

0 Asked on January 10, 2021

2 Asked on January 10, 2021 by stats_nerd

feature engineering feature selection machine learning regression

0 Asked on January 10, 2021 by anto_zoolander

2 Asked on January 10, 2021 by snoopy

Get help from others!

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

Recent Answers

- Joshua Engel on Why fry rice before boiling?
- Jon Church on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP