1. Economics of agro-food safety and international market for agro-food products and legislation
Antonio Stasi

2. INDEX Regression: a general set-up Linear regression
Linear regression by OLS
What about more variables
Beyond the lines
Measures of fit
Variables selection
How to run a linear regression

3. Regression: a general set-up
You have a set of data on two variables, X and Y, represented in a scatter plot
You wish to find a simple, convenient mathematical function that comes close to most of the points, thereby describing succinctly the relationship between X and Y

4. Linear Regression The straight line is a particularly simple function.
When we fit a straight line to data, we are performing linear regression analysis.

5. Linear Regression The Goal:
Find the “best fitting” straight line for a set of data. Since every straight line fits the equation:
Y = bX + c
with slope b and Y-intercept c, it follows that our task is to find a b and c that produce the best fit.
There are many ways of operationalizing the notion of a “best fitting straight line.” A very popular choice is the “Least Squares Criterion.”

6. Linear Regression
For every data point , define the X, Y “predicted score” to be the value of the straight line evaluated at . The “regression residual,” or “error of prediction” is the distance from the straight line to the data point in the up-down direction.

7. Linear Regression by OLS40 20 10 20 X

8. Linear Regression by OLS40 Y
predicted 20 20 X

9. Error or “residual” Observation Prediction
Figure 1: scatter(1:20,10+(1:20)+2*randn(1,20),'k','filled'); a=axis; a(3)=0; axis(a); 20

10. What about more variables?26 24
Temperature 22 20 30 40 20 30 10 20 10

11. What about more variables?10 20 30 40 22 24 26
Same Story, Same Procedure
Temperature
Y = c + b1X + b2 Temperature

12. Beyond lines still linear in X Y = c + b1 X + b2 X210 20 40
still linear in X
everything is the same with

13. Beyond the lines Use of LOGARITHM
Both sides of equality sign = b are elasticities
Only left hand side = b are percentages of the Y

14. Measures of fit R-square St. error T-test and P-value
Measures the percentage of data variability explained by the linear regression
St. error
Measures the dispersion (variability) of parameters
T-test and P-value
Measures whether that value of the parameter significantly predict the Y, the P- value indicates the probability of committing a mistake when I say that the parameter is significant
F-test and P-value
Measures whether the model is overall good

15. Variables selection
Structural variables should be included in the model
Variables from economic theory, e.g. education vrb when I wanna predict income
For other variables
One man One rule…When the P-value relative to the variable is < 0.15 I keep the variable

16. How to run a linear regression
Download poptools from the internet
It is a add-in (componente aggiuntiva), so you must install it jointly with your excel software
Go to extra-stats
Select regression
Select X variables matrix, select Y vector and run

17. Boosting Adult System Education In Agriculture – AGRI BASE
Financed by:
Partners: