Читать книгу Introduction to Linear Regression Analysis - Douglas C. Montgomery - Страница 3
List of Illustrations
Оглавление1 Chapter 1Figure 1.1 (a) Scatter diagram for delivery volume. (b) Straight-line relation...Figure 1.2 How observations are generated in linear regression.Figure 1.3 Linear regression approximation of a complex relationship.Figure 1.4 Piecewise linear approximation of a complex relationship.Figure 1.5 The danger of extrapolation in regression.Figure 1.6 Acetone–butyl alcohol distillation column.Figure 1.7 The designed experiment for the distillation column.Figure 1.8 Regression model-building process.
2 Chapter 2Figure 2.1 Scatter diagram of shear strength versus propellant age, Example 2....Figure 2.2 Situations where the hypothesis H0: β1 = 0 is not rejected.Figure 2.3 Situations where the hypothesis H0: β1 = 0 is rejected.Figure 2.4 The upper and lower 95% confidence limits for the propellant data....Figure 2.5 The 95% confidence and prediction intervals for the propellant data...Figure 2.6 Scatter diagram of satisfaction versus severity.Figure 2.7 JMP output for the simple linear regression model for the patient s...Figure 2.8 JMP output for the model relating team wins to team ERA for the 201...Figure 2.9 Two influential observations.Figure 2.10 A point remote in x space.Figure 2.11 An outlier.Figure 2.12 Scatter diagrams and regression lines for chemical process yield a...Figure 2.13 True relationship between yield and temperature.Figure 2.14 Scatter diagram of shelf-stocking data.Figure 2.15 The confidence and prediction bands for the shelf-stocing data.
3 Chapter 3Figure 3.1 (a) The regression plane for the model E(y) = 50 + 10x1 + 7x2. (b) ...Figure 3.2 (a) Three-dimensional plot of regression model E(y) = 50 + 10x1 + 7Figure 3.3 (a) Three-dimensional plot of the regression model , (b) The conto...Figure 3.4 Scatterplot matrix for the delivery time data from Example 3.1.Figure 3.5 Three-dimensional scatterplot of the delivery time data from Exampl...Figure 3.6 A geometrical interpretation of least squares.Figure 3.7 A matrix of scatterplots.Figure 3.8 Joint 95% confidence region for β0 and β1 for the rocket ...Figure 3.9 JMP output for the multiple linear regression model for the patient...Figure 3.10 JMP output for the model relating team wins to team ERA and team e...Figure 3.11 An example of extrapolation in multiple regression.Figure 3.12 Scatterplot of cases and distance for the delivery time data.Figure 3.13 Data on two regressors.Figure 3.14 (a) A data set with multicollinearity. (b) Orthogonal regressors....Figure 3.15 Sampling distribution of .Figure 3.16 Plot of y versus x1.
4 Chapter 4Figure 4.1 Example of a pure leverage point.Figure 4.2 Example of an influential point.Figure 4.3 Normal probability plots: (a) ideal; (b) light-tailed distribution;...Figure 4.4 Normal probability plot of the externally studentized residuals for...Figure 4.5 Patterns for residual plots: (a) satisfactory; (b) funnel; (c) doub...Figure 4.6 Plot of externally studentized residuals versus predicted for the d...Figure 4.7 Plot of externally studentized residuals versus the regressors for ...Figure 4.8 Prototype residual plots against time displaying autocorrelation in...Figure 4.9 Partial regression plots for the delivery time data.Figure 4.10 Plot of xi versus xj.Figure 4.11 Plot of regressor x1 (cases) versus regressor x2 (distance for the...Figure 4.12 Plot of externally studentized residuals by site (city) for the de...Figure 4.13 Externally studentized residual plots for the rocket propellant da...Figure 4.14 Residual plots for the rocket propellant data with observations 5 ...Figure 4.15 Data illustrating lack of fit of the straight-line model.Figure 4.16 JMP output for the simple linear regression model relating satisfa...
5 Chapter 5Figure 5.1 Scatter diagram of the energy demand (kW) versus energy usage (kWh)...Figure 5.2 Plot of R-student values ti versus fitted values , Example 5.1.Figure 5.3 Plot of R-student values ti versus fitted values for the transfor...Figure 5.4 Linearizable functions. (From Daniel and Wood [1980], used with per...Figure 5.5 Plot of DC output y versus wind velocity x for the windmill data.Figure 5.6 Plot of residuals ei versus fitted values for the windmill data....Figure 5.7 Plot of DC output versus x′ = 1/x for the windmill data.Figure 5.8 Plot of R-student values ti versus fitted values for the transfor...Figure 5.9 Plot of residual sum of squares SSRes(λ) versus λ.Figure 5.10 Plot of ordinary least-squares residuals versus fitted values, Exa...Figure 5.11 Plot of weighted residuals versus weighted fitted values , Exam...Figure 5.12 JMP results for the delivery time data treating city as a random e...
6 Chapter 6Figure 6.1 An example of a leverage point.Figure 6.2 An example of an influential observation.
7 Chapter 7Figure 7.1 An example of a quadratic polynomial.Figure 7.2 Danger of extrapolation.Figure 7.3 Scatterplot of data, Example 7.1.Figure 7.4 Plot of residuals ei, versus fitted values , Example 7.1.Figure 7.5 Normal probability plot of the residuals, Example 7.1.Figure 7.6 Scatterplot of voltage drop data.Figure 7.7 Plot of residuals ei, versus fitted values for the cubic spline m...Figure 7.8 Plot of residuals ei, versus fitted values for the cubic polynomi...Figure 7.9 Piecewise linear regression: (a) discontinuity at the knot; (b) con...Figure 7.10 The loess fit to the windmill data from SAS.Figure 7.11 The loess fit to the windmill data from JMP.Figure 7.12 The residuals versus fitted values for the loess fit to the windmi...Figure 7.13 The normal probability plot of the residuals for the loess fit to ...Figure 7.14 Central composite design for the chemical process example.Figure 7.15 Normal probability plot of the studentized residuals, chemical pro...Figure 7.16 Plot of studentized residuals versus predicted conversion, chemica...Figure 7.17 Plot of the studentized residuals run order, chemical process exam...Figure 7.18 (a) Response surface of predicted conversion. (b) Contour plot of ...Figure 7.19 (a) Response surface plot of . (b) Contour plot of .
8 Chapter 8Figure 8.1 Response functions for the tool life example.Figure 8.2 Plot of tool life y versus lathe speed x1 for tool types A and B.Figure 8.3 Plot of externally studentized residuals t versus fitted values , ...Figure 8.4 Normal probability plot of externally studentized residuals, Exampl...Figure 8.5 Response functions for Eq. (8.4).
9 Chapter 9Figure 9.1 Levels of family income and house size for a study on residential e...Figure 9.2 Contact time versus reactor temperature, acetylene data. (From Marq...Figure 9.3 Predictions of percentage of conversion within the range of the dat...Figure 9.4 Sampling distribution of (a) unbiased and (b) biased estimators of Figure 9.5 Ridge trace for acetylene data using nine regressors.Figure 9.6 Performance of the ridge model with k = 0.032 in prediction and ext...Figure 9.7 A geometrical interpretation of ridge regression.Figure 9.8 JMP output for ridge regression model for the acetylene data.Figure 9.9 JMP output for LASSO model for the acetylene data.Figure 9.10 JMP output for the elastic net model for the acetylene data.
10 Chapter 10Figure 10.1 Plot of versus p.Figure 10.2 Plot of MSRes(p) versus p.Figure 10.3 A Cp plot.Figure 10.4 Plot of versus p, Example 10.1.Figure 10.5 Plot of MSRes(p) versus p, Example 10.1.Figure 10.6 The Cp plot for Example 10.1.Figure 10.7 JMP computer output for all possible regressions, Hald Cement Data...Figure 10.8 Forward selection results from Minitab for the Hald cement data.Figure 10.9 Backward selection results from Minitab for the Hald cement data....Figure 10.10 Stepwise selection results from Minitab for the Hald cement data....Figure 10.11 Flowchart of the model-building process.Figure 10.12 Normal probability plot of the residuals for the asphalt data.Figure 10.13 Residuals versus the fitted values for the asphalt data.Figure 10.14 Residuals versus the log of the viscosity for the asphalt data.Figure 10.15 Residuals versus surface for the asphalt data.Figure 10.16 Residuals versus base for the asphalt data.Figure 10.17 Residuals versus run for the asphalt data.Figure 10.18 Residuals versus fines for the asphalt data.Figure 10.19 Residuals versus voids for the asphalt data.Figure 10.20 Normal probability plot of the residuals for the asphalt data aft...Figure 10.21 Residuals versus the fitted values for the asphalt data after the...Figure 10.22 Residuals versus the log of the viscosity for the asphalt data af...Figure 10.23 Residuals versus surface for the asphalt data after the log trans...Figure 10.24 Residuals versus base for the asphalt data after the log transfor...Figure 10.25 Residuals versus run for the asphalt data after the log transform...Figure 10.26 Residuals versus fines for the asphalt data after the log transfo...Figure 10.27 Residuals versus voids for the asphalt data after the log transfo...
11 Chapter 11Figure 11.1 Scatterplot of delivery volume x1 versus distance x2, Example 11.3...Figure 11.2 Estimation data (×) and prediction data (•) using orthonormalized ...
12 Chapter 12Figure 12.1 Contours of the residual-sum-of-squares function: (a) linear model...Figure 12.2 Plot of reaction velocity versus substrate concentration for the p...Figure 12.3 (a) Plot of inverse velocity versus inverse concentration for the ...Figure 12.4 Plot of fitted nonlinear regression model, Example 12.5.Figure 12.5 Plot of residuals versus predicted values, Example 12.5.Figure 12.6 Normal probability plot of residuals, Example 12.5.Figure 12.7 A geometric view of linearization: (a) the first iteration; (b) ev...
13 Chapter 13Figure 13.1 Examples of the logistic response function: (a) E(y) = 1/(1 + e−6....Figure 13.2 A scatter diagram of the pneumoconiosis data from Table 13.1.Figure 13.3 The fitted logistic regression model for pneumoconiosis data from ...Figure 13.4 Normal probability plot of the deviance residuals.Figure 13.5 Plot of deviance residuals versus estimated probabilities.Figure 13.6 Logit, probit, and complimentary log-log functions for the linear ...Figure 13.7 Plots of the deviance residuals from the GLM for the worsted yarn ...
14 Chapter 14Figure 14.1 Plot of residuals versus time for the soft drink concentrate sales...Figure 14.2 Plot of residuals versus time for the soft drink concentrate sales...
15 Chapter 15Figure 15.1 A scatter diagram of a sample containing an influential observatio...Figure 15.2 The double-exponential distribution.Figure 15.3 Robust criterion functions.Figure 15.4 Robust influence functions: (a) least squares; (b) Huber’s t funct...Figure 15.5 Normal probability plots from least-squares fits: (a) least square...Figure 15.6 Normal probability plots from robust fits: (a) robust fit with all...Figure 15.7 Scatterplot of observed and actual temperatures, Example 15.2.Figure 15.8 Histogram of bootstrap , Example 15.3.Figure 15.9 Histogram of bootstrap estimates , Example 15.4.Figure 15.10 Histogram of bootstrap estimates , Example 15.4.Figure 15.11 The tree partition analysis from JMP for the gasoline mileage dat...Figure 15.12 Artificial neural network with one hidden layer.Figure 15.13 The central composite design for k = 2 and .Figure 15.14 The central composite design for k = 3 and .Figure 15.15 The Box–Behnken design for k = 3 factors with one center point.Figure 15.16 Fraction of design space plot for the D-optimal and I-optimal des...
