# Category Archives: Statistical Tools

## Use of regression analysis

What is Regression?

The statistical process with the help of which we are in position to predict (or estimate) the values of one variable-called “Dependent Variable” from known values of another variable(s) – called “Independent Variable(s)” is known as Regression.

For example, if we know that the effort and size in a software project are correlated, we may find out the expected amount of effort for a given size of project.

When there is more than one independent variable, its called “Multiple Regression”.

What is Regression analysis?

Regression Analysis is a method of finding the line of best fit for a set of data.

It is a mathematical procedure that produces two results.

First it produces an equation to match the data gathered. There are different types of analysis (linear, quadratic, cubic, exponential, etc.). So one may want to check them to see which one matches the collected data most closely.

Second, regression analysis (or multiple regression analysis, if more than one independent variables are involved) may produce numbers to indicate how closely the new formula fits the data.

For example, the dependent variable might be overall satisfaction and the independent variables be price, quality, value for money, delivery time and staff knowledge.

The multiple regression analysis would then identify the relationship between the dependent variable and the independent variables – this is presented as an equation or model (formula) that might look like this:

Overall satisfaction = 1.37 * price rating + 0.91 * quality rating + 0.64 * delivery time rating + 2.42 (a constant)

Approach to Regression Analysis

The standard approach in regression analysis is:

Gather/take data –  Past data for given independent variable(s) and corresponding dependent variable is collected.

Determine the form of equation to fit – We plot the dependent and independent data sets (in case of multiple independent variables, take one variable at a time) on a special graph called a scatter plot which shows the existence (or otherwise) of statistical relationships between variables. Examine the pattern being formed by these sets.

Fit an equation – Depending on the number of independent variables, a simple (Y=a + bX) or multiple regression equation (Y = a + b1*X1 + b2*X2 + … + bp*Xp) is selected.

Evaluate the fit using statistics – such as Coefficient of Determination (R), Standard Error of Estimate (SE), etc.

The first number is the correlation coefficient, r. This is the linear correlation coefficient, for use in indicating how closely the data fits a straight line. The closer r is to 1 (for a positive correlation) or -1 (for a negative correlation) the better the fit. A value of 0 indicates no fit at all.

Second is R (r2), the coefficient of determination, which indicates how closely the curve fits the data. It’s values range from 0 to 1, with 1 being a perfect fit.

Standard error of estimate is a measure developed to measure the reliability and accuracy of the regression equation to predict the value of dependent variable for a given value(s) of independent variable(s). It measures the variability of the observed values of dependent variable (Y) around the regression line.

Use the equation to predict the value of dependent variable for given value(s) of independent variable(s).

## A Disciplined Approach To Value Stream Mapping

Value stream mapping is a very powerful tool. Used properly it will change your whole company for the better. It is not hard to use, but it does require good training and a disciplined approach.

Structure Works

Many companies today are using value stream mapping as their premier tool to develop a future state implementation plan. However, some common ‘process’ problems that hinder or even stop progress in companies around the world. Here are some of them:

1. Not taking the time to properly define product families.  If this is not done properly, then there are often false starts and confusion as people try to “become the product” to do value stream mapping. “Which product do we follow?” “What inventory do we count?”

2. Not collecting the right data on the current state map.  Customer, supplier, inventory, and process data are the building blocks for your future state plan. Without good, detailed information you cannot hope to really ‘see’ how to improve flow. Sweating a few details gives you the information needed to improve.

3. Ignoring the information flow.  Many maps that we see look more like block diagrams than value stream maps. Remember that a value stream map shows both information and material flows. An experienced mapper can plainly see how the information flow is actually creating waste in the material flows.

4. Forgetting about the timeline at the bottom of the map.  Remember that one of the major goals is to reduce lead times. When you do this, the amount of chaos and costs on your work floor also go down in proportion. You need this timeline as a baseline, and also to help prioritize improvements.

5. Companies draw a current state map, but stop there and don’t create a future state map.  They miss the whole point. If the complete approach is followed with discipline, it leads directly to a comprehensive implementation plan. Drawing a current state map (only) is of no value on its own.

6. Designing an ideal state (only).  Often companies create a future state map that represents a picture of where they would like to be ideally, in the long term. Then they have real difficulties because they find it impossible to attain this ideal state in one fell swoop. Too much to bite off at one time. It’s necessary to have this long term vision in the form of an ideal state map, but you also need shorter term future states that represent attainable goals in the near term – say 6 months to one year. This moves you ahead in manageable ‘bite-sized’ pieces.

7. Teams develop a future state map, but then don’t translate the future state map into a project plan and provide the focus to actually implement the plan.   A value stream plan has to be managed like a project, with visible progress, and regular reviews. Otherwise the ‘power’ of this approach is lost. Implementation is where the ball is most often dropped.

8. Failure to put someone in charge.  The best results we have seen are where there is a defined value stream manager that brings a focus to the achievement of the plan. Leaving the plan to a team or grouping of departments will ensure very slow progress.

9. Thinking that when the plan is implemented that you can stop there.  There is always more waste – so start on the next iteration of the future state map. You can never ‘check off’ lean as completed.