Lec10.MultiReg - Multiple Regression KNNL Chapter 6 6.1...

Info icon This preview shows pages 1–19. Sign up to view the full content.

View Full Document Right Arrow Icon
Multiple Regression KNNL Chapter 6 6.1 Intro 6.2 Matrix 6.5 ANOVA 6.6 Parameters 6.7 Mean Response 6.8 Diagnostics 6.9 Example
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Multiple Predictors Single Response ε Y + = + + = + + + + + = - = i p k ki k i i i i i i i x y x x x x y ε β β ε β β β β β 1 1 0 4 4 3 3 2 2 1 1 0
Image of page 2
Coal-Ash Data Robena Mine, Greene County, PA Gomez and Hazen (1970) Cressie (1993) Percent coal-ash 208 coal-ash cores 2500 ft spacing
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Coal-Ash Data (coal.ash.txt) coal.ash     x  y  coal   1  1 14 10.21  2  1 15  9.92  3  1 16 11.17  4  2  8 10.01  5  2 10 11.15  6  2 11 11.31  7  2 12  9.92  8  2 14 10.73  9  2 15 10.82 10  2 16 10.14
Image of page 4
x y 5 10 15 5 10 15 20 y vs. x
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Percent Coal Ash x y 5 10 15 5 10 15 20 10.21 9.92 11.17 10.01 11.15 11.31 9.92 10.73 10.82 10.14 9.97 9.93 11.65 9.46 12.5 11.05 9.41 9.91 10.82 8.23 10.39 10.41 9.76 10.93 9.79 10.74 11.21 9.7 10.27 8.96 9.35 9.63 10.11 9.37 10.17 11.75 11.04 11.11 10.82 11.1 10.94 9.64 9.29 10.59 10.43 8.75 9.52 9.53 10.8 17.61 10.96 10.28 9.78 10.55 11.21 11.46 10.82 9.78 9.88 10.21 9.84 9.89 12.8 9.06 10.39 9.32 8.96 10.06 10.61 8.86 10.87 10.83 13.07 11 11.61 9.93 10.41 10.12 10.38 8.9 11.09 10.29 10.34 10.03 10.7 10.65 8.27 12.65 10.27 9.48 10.09 10.47 9.79 9.16 10.7 8.45 9.4 9.79 10.18 10.63 9.84 8.2 9.36 11.21 10.36 11.62 8.14 9.63 9.59 9.22 13.06 8.69 11.58 10.19 10.04 9.27 8.9 9.48 8.91 9.34 8.82 10.01 9.82 8.57 8.98 9.58 10.91 9.82 9.61 11.41 11.17 9.46 9.15 11.19 9.28 8.07 10.99 9.22 10.56 10.18 9.01 10.06 9.01 9.27 10.66 8.76 7.81 8.2 9.96 9.39 8.54 8.15 8.1 10.13 7.96 9.92 11.43 9.06 9.34 7.68 8.58 9.04 8.19 8.92 8.89 8.59 9.15 9.56 10.87 9.2 11.3 8.61 7 7.85 8.61 9.25 8.89 7.28 7.88 7.8 9.1 9 8.78 7.9 8.21 7.83 8.64 9.58 7.61 7.84 7.62 11.86 9.14 7.04 9.69 8.2 9.03 9.65 8.91 8.81 9.96 8.77 8.6 9.99 7.63 7.95 9.91 9.07
Image of page 6
X -5 0 5 10 15 20 5 10 15 20 Y Percent Coal Ash 8 10 12 14 16 18
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
x coal 5 10 15 8 10 12 14 16 18 coal vs. x
Image of page 8
y coal 5 10 15 20 8 10 12 14 16 18 coal vs. y
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Multiple Regression on Coal Ash error NS EW Intercept l PercentCoa x x y i i i i + + + = + + + = ε β β β 2 2 1 1 0
Image of page 10
Splus Linear Model coal.lm = lm(coal~x+y,data=coal.ash) # summary(coal.lm) Coefficients:                Value Std. Error  t value Pr(>|t|)  (Intercept)  11.2468   0.2250    49.9818   0.0000           x  -0.1771   0.0252    -7.0332   0.0000           y  -0.0104   0.0141    -0.7368   0.4621
Image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
x coal 5 10 15 8 10 12 14 16 18 coal vs. x i i x y 1 1 0 ˆ β β + =
Image of page 12
y coal 5 10 15 20 8 10 12 14 16 18 coal vs. y i i x y 2 2 0 ˆ β β + =
Image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
coal vs. x and y
Image of page 14
Higher Order Effects Multiple Regression Polynomial Regression i i i i i i i i i i i i x x x x y x x x x y ε β β β β β ε β β β β β + + + + + = + + + + + = 4 4 3 3 2 2 1 0 4 4 3 3 2 2 1 1 0
Image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Interaction Multiple Regression with Higher Order Effects 2 1 3 2 2 1 1 0 i i i i i i x x x x y ε β β β β + + + + =
Image of page 16
No Interaction vs. Interaction x coal 5 10 15 8 10 12 14 16 18 x coal 5 10 15 8 10 12 14 16 18 No Interaction Interaction
Image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
lines(supsmu(coal.ash$x[coal.ash$y<=10],coal.ash$coal[coal.ash$y<=10],span=.75),lwd=3,col=2) lines(supsmu(coal.ash$x[coal.ash$y>10],coal.ash$coal[coal.ash$y>10],span=.75),lwd=3,col=2) x coal 5 10 15 8 10 12 14 16 18
Image of page 18
Image of page 19
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern