Data Analysis

DATA ANALYSIS I

FUNCTIONS & DESCRIPTIVE STATISTICS

I. FUNCTIONS (Barnett, Chapter 1)

A. INDEPENDENT (input) VS. DEPENDENT (output) VARIABLES:

1. Examples:

a. The effect of Price on Quantity of Items sold:

b. The carrying/book value of an asset as time passes:

B. LINEAR FUNCTIONS - OVERVIEW:

1. The Equation:

a. slope: "RISE OVER RUN"

b. y intercept: THE VALUE OF Y WHEN X EQUALS 0

c. x intercept: THE VALUE OF X WHEN Y EQUALS 0

C. WORKING WITH LINEAR FUNCTIONS:

1. Estimating the Equation Model Ð'- Simple Example:

You want to analyze the relationship between advertising expenditures

sales. You have been given the following information:

Month Advertising

Expenditures

Sales

May $ 6,000 $18,000

June $ 2,000 $10,000

July $ 4,000 $14,000

a. The Function:

b. The Slope:

c. The Y Intercept:

d. The X Intercept:

e. The Equation:

f. The Graph:

y

x

2. Projections using the estimated equation:

Month Projected

Advertising

Expenditures

Projected

Sales

August $ 5,000 $

Sept. $ 3,000 $

October $ 4,000 $

II. NUMERICAL DESCRIPTIVE MEASURES (Levine, Chapters 3 & 7)

A. Measures of Central Tendency and Variation:

1. Arithmetic Mean:  x i _

n = x

2. The Range: highest value - lowest value

3. Variance = the average of the squared deviations from the mean

1. Population Variance:

σ2 =  (x - Ð'µ)2

N

2. Sample Variance:

_

s2 =  (x - x)2

n - 1

4. Standard deviation = "Standard Error" = the positive square root of the variance

1. Population Standard Deviation:

_____

σ = (σ2)1/2 = √ σ2

2. Sample Standard Deviation:

____

s = (s2) 1/2 = √ s2

5. Example: Levine Ch3 homework problem 3.20 (page 130)

B "Degrees of Freedom" (df)

Example: We have 6 sample values that have a mean of 15. The fact that

n = 6 and average x = 15 also tells us that:

 xi = 90 = (15 * 6)

because

 x i _

n