My final contribution - the key to this is not to over- fit, so cross validate on the training sample; tree regression has this built in. If the X's are correlated then consider ridge regression which aims to reduce MSE .

Of course if you were out of the machine learning environment - you would have to think theoretically and conceptually - I am being rude again!

Allow it to be more flexible, like non-linear? Include more information in your model?

I'm not sure that you have phrased your question the way you intend. Do you mean how to assess the "accuracy"?, what do you mean by "accuracy"?, etc. I gave very broad answers, basically just if you have more dfs in your model at least some measures of accuracy will likely increase (and you can examine this through things like cross validation or looking at R^2), but I don't know if you are really after some more specific answer.

Dear Dr., Daniel Wright I'm extremely sorry for the inconvenience. Actually, I have a machine learning project with python by using a scikit-learn library. I have two separate datasets for training and testing and I try to do linear regression. How can I increase my accuracy? (like, adding code, parameter, normalize data or regularisation, etc.)

accuracy of what? I hope that this is not rude, but accuracy does not equate to precision, and the two need to be distinguished. In that sense ,inaccuracy of parameter equals bias so that as Daniel points out, the unknown functional form of the estimated model has to be correct, which is a big ask.

on the difference see https://chemistrygod.com/accuracy-and-precision-in-chemistry

your second post came in as i was writing my reply, you have a controlled situation so you may be interested in mean square error in going from the training sample to the testing sample. https://en.m.wikipedia.org/wiki/Mean_squared_error This will allow you to evaluate you potential improvements.

Dear Dr., Kelvyn Jones It's completely fine. I'm extremely sorry for the inconvenience. I forgot to clarify the question. Actually, I have a machine learning project with python by using a scikit-learn library. I have two separate datasets for training and testing and I try to do linear regression. How can I increase my accuracy? (like, adding code, parameter, normalize data or regularisation, etc.)

Thank you very much, Dr. Kelvyn Jones, for your suggestion.

My final contribution - the key to this is not to over- fit, so cross validate on the training sample; tree regression has this built in. If the X's are correlated then consider ridge regression which aims to reduce MSE .

Of course if you were out of the machine learning environment - you would have to think theoretically and conceptually - I am being rude again!

Don't think of Kelvyn Jones ' final sentence as being rude, but as a plea for those only looking at things like predictive accuracy (however defined) to consider inside the model and having that perhaps approximate what actual may be occurring in nature. Pearl has a brief piece on this (http://ftp.cs.ucla.edu/pub/stat_ser/r489.pdf), and the https://web.stanford.edu/~hastie/CASI/ can be seen as an argument for this too. They contrast statistics with data science, and depending on who says "machine learning" it is closer to one or the other of these. Here is what they say in their preface:

" Very broadly speaking, algorithms are what statisticians do while inference says why they do them. A particularly energetic brand of the statistical enterprise has flourished in the new century, data science, emphasizing algorithmic thinking rather than its inferential justification."

I could go on a bit, but this is already taking discussion beyond the question.

Please look at the following below links which may help you in your analysis:

https://www.jigsawacademy.com/5-super-tips-to-improve-your-linear-regression-models/

https://datascience.stackexchange.com/questions/30465/tips-to-improve-linear-regression-model

https://www.analyticsvidhya.com/blog/2015/12/improve-machine-learning-results/

Thanks

Hi, Dewan,

One option is to select a paradigm which by design explicitly maximizes (weighted) classification accuracy as assessed in validity.

What is maximum accuracy?

• https://odajournal.com/2014/04/06/a-statistical-guide-for-the-ethically-perplexed-chapter-4-panter-sterba-handbook-of-ethics-in-quantitative-methodology-routledge-2011-clarifying-disorientation-regarding/

This little article helps visualize model accuracy in the present context:

• https://odajournal.com/2018/11/26/visualizing-application-and-summarizing-accuracy-of-oda-models/

What is the new paradigm?

• https://odajournal.com/2020/06/28/what-is-novometric-data-analysis/

Is there an example?

• https://odajournal.com/2016/09/19/novometric-analysis-with-ordered-class-variables-the-optimal-alternative-to-linear-regression-analysis/

Do maximum-accuracy models over-fit in training analysis (even though the accuracy of the model is actually assessed in validity analysis)? No, the opposite of this question is all true, however:

• https://odajournal.com/2019/03/21/some-machine-learning-algorithms-find-relationships-between-variables-when-none-exist-cta-doesnt/
• https://odajournal.com/2019/05/16/logistic-discriminant-analysis-and-structural-equation-modeling-both-identify-effects-in-random-data/
• https://odajournal.com/2019/04/22/multi-layer-perceptron-neural-net-model-identifies-effect-in-random-data/
• https://odajournal.com/2019/04/11/effect-of-sample-size-on-discovery-of-relationships-in-random-data-by-classification-algorithms/

Thank you so much Dr. Paul Yarnold for your help.

Thank you so much Dr. Daniel Wright for your help.

Thank you so much Dr. Isam Eldin Hussein Elgailani for your help.

Thank you also very much, and best regards, Dr's Dewan Azmal Hossain and Daniel Wright

1) If the number of X's, n, is large, the MSE is small and, hence, the variances of the slope, intercept and predition interval are also small. However, the number n can not increase infinitely; in the case of the univariate linear calibration, I think, the appropriate number n is 5. (I regard "the number 5" as magic number of different standards in the linear calibration.)

2) In the case of linear calibration, the accuracy of the standards to be used for the calibration will make the linear calibration more accurate.

It is also important to know the statistical properties of the regression model to be used (that is, "simple linear regression" or "reversed inverse regression").

On Kelvyn Jones comment (and mine right below him), this ( https://www.tandfonline.com/doi/pdf/10.1080/01621459.2020.1762613?needAccess=true ) just came out in JASA and is a good discussion of the differences by Efron.

Thank you Dr. Daniel Wright for giving me the opportunity to read the article. Prediction, Estimation, and Attribution is an excellent Article.

You can first explore the data and determine it's distribution, then you can transform the data appropriately (like standardize, log, shift, etc) with respect to the distribution