Essay About S2 And Standard Deviation

Data Analysis
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DATA ANALYSIS I
FUNCTIONS & DESCRIPTIVE STATISTICS
I. FUNCTIONS (Barnett, Chapter 1)
INDEPENDENT (input) VS. DEPENDENT (output) VARIABLES:
Examples:
The effect of Price on Quantity of Items sold:
b. The carrying/book value of an asset as time passes:
LINEAR FUNCTIONS – OVERVIEW:
The Equation:
slope: “RISE OVER RUN”
y intercept: THE VALUE OF Y WHEN X EQUALS 0
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
$ 6,000
$18,000
$ 2,000
$10,000
$ 4,000
$14,000
The Function:
The Slope:
The Y Intercept:
The X Intercept:
The Equation:
The Graph:
y
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)
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 – е)2
N
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