The Assembly Department Manager (the same one as used before) now concerned about the scrap rate that he sees on the Quarterly Scrap Rate Report for his department. The weekly scrap rate data is shown here.
Week Scrap/ Rework
Your first instinct is to analyze this data is to see if there is a correlation between the scrap rate and the production of good pieces or the amount of hours worked. So you match up week for week the scrap rate and the production output to determine the correlation. And then you do it again with the hours worked.
Assignment: Choose either the Production data or the Hours Worked data from Case 2. Do a correlation analysis of this data with the Scrap Rate.
Assignment Expectations: Do the following:
? a. Calculate the Coefficient of Determination
? b. Calculate the Coefficient of Correlation
? c. Calculate the Covariance and show the alternate calculation
? d. Test the significance of the Correlation Coefficient
? e. Generate the Data Analysis using the Excel Covariance Data Analysis
Write a two page paper explaining what you did and interpret the results of the correlation analysis. Be sure to reference the results of the data analysis for both correlation calculations. Include other references that you use. Submit the paper as the case and upload the Excel file into Additional files.
The assigned reading is Schaum's Outline of Business Statistics, 4th Edition, Ch. 14, Sections 14.9 - 14.13, and Chapter Problems 14.12 to 14.15 at the end of the chapter. This text is available on ebrary; Kazmier, Leonard J. Schaum's Outline of Business Statistics, 4th Edition. Blacklick, OH, USA: McGraw-Hill Trade, 2003. p 271. Retrieved 11/14/09 from http://site.ebrary.com/lib/touro/Doc?id=10051516&ppg=289.
14.9 Objectives and Assumptions of Correlation Analysis introduces the topic.
14.10 The Coefficient of Determination discusses the amount of the variance in the dependent variable that is explained by the independent variable. See Problem 14.12
14.11 The Coefficient of Correlation, which is the square root of the Coefficient of Determination, lends itself to statistical testing. See Problem 14.13
14.12 The Covariance approach to understanding correlation discusses how to measure the extent to which two variables "vary together". See Problem 14.14
14.13 Significance testing with respect to the Correlation Coefficient discusses hypothesis testing. See Problem 14.15
There are some pitfalls to consider when using regression analysis. These are discussed in section 14.14 along with pitfalls of correlation (Module 2). Those pitfalls are shown here.
(4) A significant correlation coefficient does not necessarily indicate causation, but rather may indicate a common linkage to other events.
(5) A significant correlation is not necessarily an important correlation. Given a large sample, a correlation of, say, r = +0.10 can be significantly different from 0 at α = 0.05. Yet the coefficient of determination of r2 = 0.01 for this example indicates that only 1 percent of the variance in Y is statistically explained by knowing X.
(6) The interpretation of the coefficients of correlation and determination is based on the assumption of a bivariate normal distribution for the population and, for each variable, equal conditional variances.
(7) For both regression and correlation analysis, a linear model is assumed. For a relationship that is curvilinear, a transformation to achieve linearity may be available. Another possibility is to restrict the analysis to the range of values within which the relationship is essentially linear.
We have the data for the scrap rate which is by week for one quarter and for which we need to perform correlation analysis. The Assembly Manager would use the data for the amount of hours worked to test if there is any correlation between the scrap rate and the amount of hours worked. For this we would calculate the coefficient of correlation for the data which is used to determine the strength of the relationship between two variables. For our data, we get the coefficient of correlation as 0.10565 which indicates that the relationship between the scrap rate and hours worked is weak. It also mean that 10.56% of the variance in scrap rate is explained by the hours worked. The relationship is however positive which means that as one variable increases, the other variable also increases.
The relationship is indicated by coefficient ...
A lean six sigma project case is examined.