notes7 - Chapter 5 Timothy Hanson Department of Statistics,...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 5 Timothy Hanson Department of Statistics, University of South Carolina Stat 704: Data Analysis I 1 / 43 Chapter 3: Diagnostics Section 3.1: Outlying x-values can be found via boxplot (or a scatterplot!) Useful for assessing extrapolation. More advanced method in Sec. 10.3 for multiple predictors. Section 3.2: Recall r i = Y i- Y i is i th residual. The (externally) studentized residual t i (defined on p. 396) has a t n- 3 distribution. Section 3.3: Plots to consider 1 Plot of r i vs. Y i or r i vs. x i : nonlinearity means line + 1 x i inappropriate. Nonconstant variance means var( i ) = 2 not appropriate. Outlying observations (very large or small residuals) can indicate several potential problems (later). 2 Histogram or boxplot of r i , normal probability plot of r i to check normality. Expect one outlier out of 150 observations for truly normal data in boxplot. There are also formal tests for normality (later). 2 / 43 5.1 Matrices A matrix is a rectangular array of numbers. Heres an example: A = 2 . 3- 1 . 4 17- 22 . 5 2 . This matrix has dimensions 2 3. The number of rows is first, then the number of columns. We can write the n p matrix X abstractly as X = x 11 x 12 x 13 x 1 p x 21 x 22 x 23 x 2 p x 31 x 32 x 33 x 3 p . . . . . . . . . . . . . . . x n 1 x n 2 x n 3 x np . 3 / 43 Other notation Another notation that is common is A = [ a ij ] n m for an n m matrix A with element a ij in the i th row and j th column. The matrix X on the previous page would then be written X = [ x ij ] n p . 4 / 43 5.1 (contd) Transpose The transpose of a matrix A takes the matrix A and makes the rows the columns and the columns the rows. Precisely, if A = [ a ij ] n m then A is the m n matrix with elements a ij = a ji . For example: If A = 1 2 3 4 5 6 , then A = 1 4 2 5 3 6 . Question: what is ( A ) ? 5 / 43 5.2 Matrix addition If two matrices A = [ a ij ] n m and B = [ b ij ] n m have the same dimensions, you can add them together, element by element, to get a new matrix C = [ c ij ] n m . That is, C = A + B is the matrix with elements c ij = a ij + b ij . For example, - 1- 2 5 7- 10 20 + 1 2 3 4 1 2 = - 1 + 1- 2 + 2 5 + 3 7 + 4- 10 + 1 20 + 2 = 8 11- 9 22 . 6 / 43 5.3 Multiplying a matrix times a number Multiplying a matrix A = [ a ij ] by a number b yields the matrix C = A b with elements c ij = a ij b . For example, (- 2) - 1- 2 5 7- 10 20 = - 1(- 2)- 2(- 2) 5(- 2) 7(- 2)- 10(- 2) 20(- 2) = 2 4- 10- 14 20- 40 ....
View Full Document

Page1 / 43

notes7 - Chapter 5 Timothy Hanson Department of Statistics,...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online