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[PDF File]10.simple linear regression
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A common notational shorthand is to write the "sum of squares of X" (that is, the sum of squared deviations of the X’s from their mean), the "sum of squares of Y", and the "sum of XY cross products" as,
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[PDF File]EXPECTED MEAN SQUARES Fixed vs. Random Effects
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EXPECTED MEAN SQUARES Fixed vs. Random Effects • The choice of labeling a factor as a fixed or random effect will affect how you will make the F-test. • This will become more important later in the course when we discuss interactions. Fixed Effect • All treatments of …
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[PDF File]Type I and Type III Sums of Squares
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Feb 04, 2003 · Also notice the relationship between the Type I tests and the omnibus test. Notice that the sum of square on line B-F add up to the SSR on line A. It can be shown algebraically that the Type I sum of squares will always add up to the sum of squares on the model line. G through K - These are the Type III tests. Just like the Type I tests, each ...
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[PDF File]Paper 1521-2015 Sums of Squares: The Basics and a Surprise
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review sum of squares basics, illustrate the importance of choosing the appropriate sum of squares type, and highlight differences in PROC GLM and PROC REG parameterization coding. INTRODUCTION . This paper began with a mystery. A researcher contacted the Statistics Outreach Center at the University of Iowa with a problem.
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[PDF File]Statistical Tolerancing
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Statistical Tolerancing Assumption • Statistical tolerancing assumes that disks are chosen at random, not deliberately to make a worst possible stack, one way or the other. • The disk thickness variation within tolerances is described by a distribution. • The histogram, summarizing these thicknesses, is often assumed to be ≈ normal or Gaussian with center µD at the middle of the ...
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[PDF File]The NPAR1WAY Procedure
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Dose N Mean-----0 16 222.187500 0.04 11 217.363636 Source DF Sum of Squares Mean Square F Value Pr > F-----Among 1 151.683712 151.683712 0.5587 0.4617 Within 25 6786.982955 271.479318 Average scores were used for ties. The NPAR1WAY Procedure Wilcoxon Scores (Rank Sums) for Variable Gain Classified by Variable Dose Sum of Expected Std Dev Mean
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[PDF File]CHAPTER 8. RANDOMIZED COMPLETE BLOCK DESIGN WITH …
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Step 3. Total sum of squares (TSS) TSS Y Y Yij CC =−ij =−= −= ΣΣ ΣΣ (..).. 2 2 4455561 31113 Step 4. Block sum of squares (SSB) and mean square (MSB). SSB k Y Y j kc C =−j =−= −= Σ ΣΣ (. ..). /. 2 2 4425392 9 44. MSB = SSB/(r-1) = 9.44/4 = 2.36 Step 5. Treatment sum of squares (SST) and mean square …
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[PDF File]Lecture 6 - ANOVA
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Partitioning Total Sum of Squares • “The ANOVA approach is based on the partitioning of sums of squares and degrees of freedom associated with the response variable Y” • We start with the observed deviations of Y i around the observed mean Y¯ Yi−Y¯
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[PDF File]CALCULATIONS IN THE ANALYSIS OF VARIANCE (ANOVA)
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Sum of Squares df Mean Square F Sig. Showing p < .001 . Title: Hand Calculation of ANOVA Author: rh232 Created Date: 2/11/2007 11:35:46 AM ...
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[PDF File]ONE-FACTOR COMPLETELY RANDOMIZED DESIGN (CRD)
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Trt = the treatment sum of squares = P a i=1 P n i j=1 (y i y ) 2 = P a i=1 n i(y y )2 If all sample sizes are equal (n ij = n), then SS trt = n P a i=1 (y i y ) 2 a 1 = the treatment degrees of freedom MS Trt = the treatment mean square = SS Trt a 1 Alternate Formulas SS T = Xa i=1 Xn i j=1 y2 ij y2 i N SS Trt = Xa i=1 n i N SS E = SS T SS Trt ...
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Sum of mean square