# 4.1. Least squares modelling in context¶

This section begins a new part: we start considering more than one variable at a time. However, you will see the tools of confidence intervals and visualization from the previous sections coming into play so that we can interpret our least squares models both analytically and visually.

The following sections, on design and analysis of experiments and latent variable models, will build on the least squares model we learn about here.

## 4.1.1. Usage examples¶

The material in this section is used whenever you need to interpret and quantify the relationship between two or more variables.

Colleague: How is the yield from our lactic acid batch fermentation related to the purity of the sucrose substrate?

You: The yield can be predicted from sucrose purity with an error of plus/minus 8%

Colleague: And how about the relationship between yield and glucose purity?

You: Over the range of our historical data, there is no discernible relationship.

Engineer 1: The theoretical equation for the melt index is non-linearly related to the viscosity

Engineer 2: The linear model does not show any evidence of that, but the model’s prediction ability does improve slightly when we use a non-linear transformation in the least squares model.

HR manager: We use a least squares regression model to graduate personnel through our pay grades. The model is a function of education level and number of years of experience. What do the model coefficients mean?

## 4.1.2. What you will be able to do after this section¶

# 4.2. References and readings¶

This section is only a simple review of the least squares model. More details may be found in these references.

**Recommended**: John Fox,*Applied Regression Analysis and Generalized Linear Models*, Sage.**Recommended**: N.R. Draper and H. Smith,*Applied Regression Analysis*, Wiley.Box, Hunter and Hunter,

*Statistics for Experimenters*, selected portions of Chapter 10 (2nd edition), Wiley.Hogg and Ledolter,

*Applied Statistics for Engineers and Physical Scientists*, Prentice Hall.Montgomery and Runger,

*Applied Statistics and Probability for Engineers*, Wiley.