Chapter 12:Linear Regression*

IntroductionRegression analysis and Analysis of variance are the two most widely used statistical procedures.Regression analysis:DescriptionPredictionEstimation*

12.1 Simple Linear Regression*(12.1)(12.2)

12.1 Simple Linear Regression*

Table 12.1 Quality Improvement Data*

MonthTime Devoted to Quality Impr.# of Non-conformingJanuary5620February5819March5520April6216May6315June6814July6615August6813September7010October6713November729December648

Figure 12.1 Scatter Plot*

Figure 12.1a Scatter Plot*

12.1 Simple Linear Regression*

12.1 Simple Linear RegressionThe regression equation isY = 55.9 - 0.641 X

Predictor Coef SE Coef T PConstant 55.923 2.824 19.80 0.000X -0.64067 0.04332 -14.79 0.000

S = 0.888854 R-Sq = 95.6% R-Sq(adj) = 95.2%

Analysis of Variance

Source DF SS MS F PRegression 1 172.77 172.77 218.67 0.000Residual Error 10 7.90 0.79Total 11 180.67

*

12.1 Simple Linear Regression*

12.2 Worth of the Prediction Equation*

ObsXYFitSE FitResidualSt Resid156.020.00020.0460.464-0.046-0.06258.019.00018.7650.3950.2350.30355.020.00020.6870.500-0.687-0.93462.016.00016.2020.286-0.202-0.24563.015.00015.5610.270-0.561-0.66668.014.00012.3580.2891.6421.95766.015.00013.6390.2611.3611.60868.013.00012.3580.2890.6420.76970.010.00011.0770.338-1.077-1.311067.013.00012.9990.2720.0010.001172.09.0009.7950.400-0.795-1.001274.08.0008.5140.470-0.514-0.68

12.2 Worth of the Prediction Equation*(12.4)

12.3 Assumptions*(12.1)

12.4 Checking Assumptions through Residual Plots*

12.4 Checking Assumptions through Residual Plots*

12.5 Confidence Intervals*

12.5 Hypothesis Test*

12.6 Prediction Interval for Y*

12.6 Prediction Interval for Y*

12.7 Regression Control Chart*(12.5)(12.6)

12.8 Cause-Selecting Control Chart*The general idea is to try to distinguish between quality problems that occur at one stage in a process from problems that occur at a previous processing step. Let Y be the output from the second step and let X denote the output from the first step. The relationship between X and Y would be modeled.

12.9 Linear, Nonlinear, and Nonparametric Profiles*Profile refers to the quality of a process or product being characterized by a (Linear, Nonlinear, or Nonparametric) relationship between a response variable and one or more explanatory variables.A possible way is to monitor each parameter in the model with a Shewhart chart.The independent variables must be fixedControl chart for R2

12.10 Inverse Regression*An important application of simple linear regression for quality improvement is in the area of calibration.Assume two measuring tools are available One is quite accurate but expensive to use and the other is not as expensive but also not as accurate. If the measurements obtained from the two devices are highly correlated, then the measurement that would have been made using the expensive measuring device could be predicted fairly from the measurement using the less expensive device.Let Y = measurement from the less expensive deviceX = measurement from the accurate device

12.10 Inverse Regression*

12.10 Inverse RegressionExample*YX2.32.42.52.62.42.52.82.92.93.02.62.72.42.52.22.32.12.22.72.7

12.11 Multiple Linear Regression*

12.12 Issues in Multiple Regression12.12.1 Variable Selection*

12.12.3 Multicollinear DataProblems occur when at least two of the regressors are related in some manner.Solutions:Discard one or more variables causing the multicollinearityUse ridge regression*

12.12.4 Residual Plots*

12.12.6 Transformations*

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