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

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

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

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

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.”

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.

Linear Regression by OLS 40 20 10 20 X

Linear Regression by OLS 40 Y predicted 20 20 X

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

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

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

Beyond lines still linear in X Y = c + b1 X + b2 X2 10 20 40 still linear in X everything is the same with

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

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

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

How to run a linear regression Download poptools from the internet http://www.cse.csiro.au/poptools/download.htm 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

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