iSixSigma

Fits

Definition of Fits:

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If you have enough data to work with, you can work with fits in a regression model as a predictor of outcomes within your dataset. This can be extremely helpful in manufacturing and other industries, as well as in everyday life.

Overview: What are fits?

Fits are another term for fitted values. A fitted value is a prediction in a statistical model of a mean response value. This comes from inputting the values of the factor levels, predictors, or components into a model. They are used to forecast observations in a time series.

3 benefits of fits

There are some major benefits of fits that you should be aware of:

Forecasting – One benefit of a fit is that it can act as a bit of a forecaster, in that it predicts an output even without observation of the specific levels of the inputs.

Results of variation – Another beneficial aspect of fits is how they allow for the exploration of how variation in inputs results in the output of interest.

Plotting residuals – You can use fits to plot residuals by placing your fitted values on the x-axis and residuals on the y-axis.

Why are fits important to understand?

Fits are important to understand for the following reasons:

Making predictions

Understanding how fits work is incredibly important because being able to make reasonably sound predictions is an incredible asset in your business.

Regression models

Having an understanding of fits gives you a more well-rounded knowledge base of how to work with regression models.

Simplification and practical knowledge

Understanding how to work with fits allows you to take the Y=F(x) relationship and display it as a simple prediction. This is helpful for not only yourself but for anyone whom you might need to explain the findings of your graph to.

Figuring in the entire data set

An important reason for understanding fits is that they take the entire set of data into account, as opposed to just a single observation. This allows you to assess more accurate long-term expectations.

An industry example of fits

A manufacturing plant wants to determine how many defects they can expect in various runs of units produced. To predict this, they look at a variety of orders that had different quantities and how many defects were logged for each. Using the data collected, they check to see if there is a statistically significant relationship between the variables. They also need to evaluate the sustainability of this regression model’s ability to make reasonably accurate predictions. When assessing the residual plots, it is found that the residuals are random, indicating that the fits are non-biased. With the data collected and plotted using a regression model, the manufacturing plant feels that it can confidently make predictions as to how many defects to expect in various quantity orders that are within the data set.

3 best practices when thinking about fits

Here are some practices to keep in mind when it comes to working with fits:

Do not overextend your predictions – Be careful not to make predictions far outside of the range of your data set.

Test – In order to ensure that your predictions are sound, it is important to test your variables in real life to see that your predictions are reasonably matching up with reality.

Use dedicated software – While you can do these sorts of calculations by hand, it is worth having software to run these types of models. This is especially true when you are working with large datasets. Also, whether you are initially working by hand or with software, you always have the other option to check against yourself.

Frequently Asked Questions (FAQ) about fits

What is the difference between a fit and a fitted value?

A fit is just another term for a fitted value.

What is the difference between a fit and a predicted value?

Fit is another term for a fitted value, which is also synonymous with a predicted value. These three terms are interchangeable.

Will my fits always match my observed data?

It is highly unlikely that your predicted values will exactly match your observed values. There are too many factors involved in real-time to ensure that your predictions will line up exactly with your observed data. Hopefully, they generally fall within a reasonable range unless there is an unpredictable change in your processes.

The power of fits

Whether you call them fits, fitted values or predicted values does not matter. The thing that is important is that you know how to work with them. Having an understanding of this concept and how to utilize it with regression models gives you the ability to make predictions that can only be an asset to your business.

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