Quiz 3: Analysis of Variance and Quadratic Effects - Prof. David Dickey, Quizzes of Statistics

Download Quiz 3: Analysis of Variance and Quadratic Effects - Prof. David Dickey and more Quizzes Statistics in PDF only on Docsity! Quiz 3 St 512 Fall 2005 Dickey 1. Here is a table of (P, M) totals for a 2x3x2 experiment with factors N (nitrogen) , P (pH), and M (moisture) at 2, 3, and 2 levels. I have also given what we called the “table sum of squares” in our notes. The experiment was a randomized complete block design with 6 blocks. P 6.5 7.0 7.5 20 M 40 Totals: 1470 2100 2730 Table SSq = 7142/12 + 8402/12 + …+14702/12 – 63002/72= 42336 (A) (10 pts.) How many observations______ do I have in all? (B) (24 pts.) Compute, if possible, the missing sums of squares and degrees of freedom for this part of the analysis of variance table. If not possible, explain. Source df Sum of Squares M 1 6272 P ____ __________ MP ____ ___________ (C) (8 pts.) Using the orthogonal polynomial coefficients 1,-2, 1 for quadratic effects, compute the sum of squares _______for testing to see if the quadratic P effect is the same at both levels of M. 2. I have a data set with 21 points (X,Y) but there are only 7 distinct values of X. Y is yield and X is temperature. I ran this code: PROC GLM; CLASS X; MODEL Y=X; Obtaining this analysis of variance (without sums of squares): ANOVA Source df Mean F Pr>F Square X ___ 800 4.00 0.0153 Error ___ _____ (A) (15 pts.) Fill in the missing degrees of freedom (df) and error mean square. (B) (5 pts.) Do I accept or reject the null hypothesis of no temperature effect on yield at the usual 5% significance level? (C) (10 pts.) If we fit a quadratic (degree 2) polynomial model to the data, how many degrees of freedom _____ would we have for lack of fit of this quadratic model? 714 840 1260 756 1260 1470