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Piecewise linear regression models

Piecewise linear regression models. Another use of interaction terms containing dummy variables. A plot demonstrating the need. The residuals versus fits plot demonstrating the need.

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Piecewise linear regression models

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  1. Piecewise linear regression models Another use of interaction terms containing dummy variables

  2. A plot demonstrating the need

  3. The residuals versus fits plot demonstrating the need

  4. and … the independent error terms i follow a normal distribution with mean 0 and equal variance 2. A formulated piecewise linear regression model • where … • yi is the compressive strength (lbs/sq in) • xi1 is the water-cement ratio (%) • xi2 is a dummy variable (0 if xi1≤ 70 and 1 if xi1 > 70) • xi2* is the (xi1-70) xi2interaction term

  5. The resulting output The regression equation is strength = 7.79 - 0.0663 ratio - 0.101 x2* Predictor Coef SE Coef T P Constant 7.7920 0.6770 11.51 0.000 ratio -0.06633 0.01123 -5.90 0.000 x2* -0.10119 0.02812 -3.60 0.003 S = 0.3286 R-Sq = 93.8% R-Sq(adj) = 93.0% Analysis of Variance Source DF SS MS F P Regression 2 24.718 12.359 114.44 0.000 Residual Error 15 1.620 0.108 Total 17 26.338

  6. The estimated regression functions

  7. The residuals versus fits plot

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