Regression and Statistical Quality Control

Question 1 

Regression analysis is a statistical process of constructing a mathematical model or function that outlines the relationship between one variable and another variable or other variables ( Fox, J. 1997) . The simple regression, also known as bivariate regression only involves two variables where one is dependent on the other. 

Question 2 

Quality has a broad range of meanings. In business, it can be termed as the ability of a product or service to deliver what it is meant to do. Quality is conformance to requirements (Crosby, P. B. 1985). For producers to provide quality products, they must fulfill all the requirements for their products. 

Question 3 

The Excel software can be used in regression analysis to create simple linear and multiple regression models so that the data can be easily analyzed ( Triola, M. F. 2013). The critical steps followed in this process are: 

After opening the excel software, you click the command button for data analysis on the data tab 

The data analysis dialogue box will then be displayed to select the regression tool. For instance, 

Select the X and Y values you want to work with 

Set the constant zero. 

Set the confidence level you want to work with. 

Select the data to be returned. 

Excel specifies that all regression variables should be in adjacent columns. For example, if the variables are in A and B columns, one of the columns must be copied so that the variables are next to each other. 

Question 4 

The control charts for R, p, c, and x ̅ can be created using the excel tool in the following manner: 

Gather the data and pick the subgroup of size n to work with. Most subsets are from 4-5. The primary purpose of this is to reduce the variation. Then set the frequency of collecting the data. The subgroups of size k should also be specified. After this, calculate the range of each subset. 

Plot the data on the x and y-axes for the charts. 

Determine the averages for all the processes. 

The final process involves analyzing the data. In doing so, variation should be considered first. Points beyond the limits show a weak relationship between the variables ( Duncan, A. J. 1974). 

Question 5 

A control chart is a type of line graph created to check the progress of processes (Ozeki & Asaka, 1996). Control charts are used to identify special certain variation causes in the manufacture of items at the time they exist. 

In the figure above, the points shown indicate the variation of performance with time. 

Question 6 

A regression model is designed to indicate the relationship between two variables. These variables are; the independent variable and the dependent variable. A plot diagram or a linear model can be used to explain this relationship. In general, plot points that are far away from each other show a weak connection and vice versa ( Fox, J. 1997). 

Question 7 

A regression analysis involving one variable against several variables is called a multiple regression ( Fox, J. 1997). A simple regression can be extended to a multiple regression by adding more dependent variables to the regression equation. This model can be written as: 

Question 8 

The door to quality enhancement is in the power of the management. The implementation of his methodologies by the management can lead to significant achievements among companies (Deming, W. E. 1981). 

Question 9 

Correlation is a measure used in statistics to show the magnitude and the direction of a link between variables. It is expressed in the form of a number. In this relationship, it is not automatic that a change in one variable implies a change in the other variables. On the other hand, causation shows that an event is a result of another event. This shows a causal relationship between variables ( Holland, P. W., Glymour, C., & Granger, C. 1985). 

References 

Besterfield, D. H., & Martin, D. (1990). Quality control (pp. 65-120). New Jersey: Prentice Hall. 

Duncan, A. J. (1974). Quality control and industrial statistics. 

Deming, W. E. (1981). Improvement of quality and productivity through action by management. Global Business and Organizational Excellence , 1 (1), 12-22. 

Holland, P. W., Glymour, C., & Granger, C. (1985). Statistics and causal inference. ETS Research Report Series , 1985 (2). 

Fox, J. (1997). Applied regression analysis, linear models, and related methods . Sage Publications, Inc. 

Triola, M. F. (2013). Elementary statistics using Excel . Pearson.