1. Statistical Methods Statistical Methods Descriptive Inferential
Statistics
Statistics
Hypothesis
Estimation
Testing

2. Inference Process Estimates & Tests Population Sample Statistics
X, Ps
Sample

3. Descriptive Statistics
Descriptive Statistics consists of the tools and techniques designed to describe data, such as charts, graphs, and numerical measures.

4. Descriptive Statistics - Examples of Descriptive Methods -
• Histograms
• Bar charts
• Average or Arithmetic Mean

5. Inferential Statistics
Inferential Statistics consists of techniques that allow a decision-maker to reach a conclusion about characteristics of a larger data set based upon a subset of those data

6. Statistical Inferences
Simple Linear Regression

7. Population Linear Regression Model
Relationship between variables is described by a linear function
The change of the independent variable causes the change in the dependent variable
Random Error
Slope
Y-Intercept  Y     X  i 1 i i
Dependent (Response) Variable
Independent (Explanatory) Variable

8. Population Linear Regression ModelY Y     X  
Observed Value i 1 i i 
= Random Error i      X YX 1 i X
Observed Value

9. Sample Linear Regression
Sample regression line provides an estimate of the population regression line as well as a predicted value of Y
Sample Y Intercept
Sample Slope Coefficient
Residual
Sample Regression Line
(Fitted Regression Line)

10. Sample Linear Regression
Using Ordinary Least Squares (OLS), we can find the values of b0 and b1 that minimize the sum of the squared residuals:
b0 provides an estimate of
b1 provides an estimate of

11. Comparison of Sample and Population Linear RegressionY X
Observations

12. Simple Linear Regression: Example
You want to examine the linear dependency of the annual sales of produce stores on their size in square footage. Sample data for seven stores were obtained. Find the equation of the straight line that fits the data best.
X Y
Annual Store Square Sales Feet ($1000)
, ,681
, ,395
, ,653
, ,543
, ,318
, ,563
, ,760

13. Scatter Diagram: Example
Excel Output

14. Least Squares Estimates
Using calculus (partial derivatives), we get
Note b is related to the correlation coefficient r (same numerator)- if x and y are positively correlated then the slope is positive

15. Equation for the Sample Regression Line: Example
By using the OLS method, we obtained:
From Excel Printout:

16. Graph of the Sample Regression Line: Example
Yi = Xi 

17. Interpretation of Results: Example
The slope of means that for each increase of one unit in X, we predict the average of Y to increase by an estimated units.
The model estimates that for each increase of one square foot in the size of the store, the expected annual sales are predicted to increase by $1.487.