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Statistical Methods for Engineers
Published in Keith L. Richards, The Engineering Design Primer, 2020
A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval. For example, weight and height, weight would be on the y-axis and height would be on the x-axis. Correlations may be positive (rising), negative (falling) or null (uncorrelated). If the pattern of dots slopes from lower left to upper right, it indicates a positive correlation between the variables being studied. If the pattern of dots slopes from upper left to lower right, it indicates a negative correlation. A line of best fit (alternatively called ‘trend line’) can be drawn in order to study the relationship between the variables. An equation for the correlation between the variables can be determined by established best-fit procedures. For a linear correlation, the best-fit procedure is known as linear regression and is guaranteed to generate a correct solution in a finite time. No universal best-fit procedure is guaranteed to generate a correct solution for arbitrary relationships. A scatter plot is also very useful when we wish to see how two comparable data sets agree to show non-linear relationships between variables. The ability to do this can be enhanced by adding a smooth line such as LOESS (Locally Weighted Scatterplot Smoothing). Furthermore, if the data is represented by a mixture model of simple relationships, these relationships will be visually evident as superimposed patterns.
Assessment of home care aides’ respiratory exposure to total volatile organic compounds and chlorine during simulated bathroom cleaning: An experimental design with conventional and “green” products
Published in Journal of Occupational and Environmental Hygiene, 2021
J. E. Lindberg, M. M. Quinn, R. J. Gore, C. J. Galligan, S. R. Sama, N. N. Sheikh, P. K. Markkanen, A. Parker-Vega, N. D. Karlsson, R. F. LeBouf, M. A. Virji
Time-weighted averages (TWA) of TVOC and chlorine air concentrations by C&D product were calculated. Smoothed airborne concentration-time profiles generated by each C&D product were then computed by combining the direct reading monitoring data across all cleaning sessions using a particular C&D product. This smoothing was performed using a non-parametric smoothing technique, Locally Weighted Regression Scatterplot Smoothing (LOWESS or LOESS) (Cleveland and Devlin 1988).
Sequential Laplacian regularized V-optimal design of experiments for response surface modeling of expensive tests: An application in wind tunnel testing
Published in IISE Transactions, 2019
Adel Alaeddini, Edward Craft, Rajitha Meka, Stanford Martinez
The proposed Laplacian regularized V-optimal design described in the previous section is developed based on the polynomial regression assumption. Hence, it is not able to discover the intrinsic geometry in the data when the data space is highly nonlinear. For this purpose, we extend the proposed methodology to Locally Weighted Scatterplot Smoothing (LOESS) (Cleveland and Devlin, 1988):