MathematicalMarketing Slide 2.1 Descriptive Statistics Chapter 2: Descriptive Statistics We will be comparing the univariate and matrix formulae for common statistical quantities.

MathematicalMarketing Slide 2.2 Descriptive Statistics The Sample Mean Vector ScalarMatrix

MathematicalMarketing Slide 2.3 Descriptive Statistics Deviation Scores ScalarMatrix

MathematicalMarketing Slide 2.4 Descriptive Statistics Sum of Squares – Conceptual Formula A = DD ScalarMatrix

MathematicalMarketing Slide 2.5 Descriptive Statistics Sum of Squares – Hand Calculator Version ScalarMatrix

MathematicalMarketing Slide 2.6 Descriptive Statistics The Variance-Covariance Matrix ScalarMatrix

MathematicalMarketing Slide 2.7 Descriptive Statistics The Variance-Covariance Matrix  It’s a key matrix It summarizes the relationship between each pair of variables.  Its orderis m · m (where m is the number of vars)  It has lots of names variance matrix, covariance matrix, variance-covariance matrix

MathematicalMarketing Slide 2.8 Descriptive Statistics The Variance-Covariance Matrix Diagonal entries could be called The S matrix is symmetric There are m (m-1) / 2 unique off diagonal elements. There are m (m+1) / 2 unique elements.

MathematicalMarketing Slide 2.9 Descriptive Statistics The Diag(·) Function

MathematicalMarketing Slide 2.10 Descriptive Statistics The Square Root of a Diagonal Matrix A unique square root of a diagonal matrix may exist. For other square or rectangular matrices, the square root is not unique.

MathematicalMarketing Slide 2.11 Descriptive Statistics Z Scores ScalarMatrix

MathematicalMarketing Slide 2.12 Descriptive Statistics The Correlation Matrix