Run the colour experiment where kids write red, green, yellow …first.

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Presentation transcript:

Run the colour experiment where kids write red, green, yellow …first

Linear Regression

In probability theory and statistics, correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables.

A scatterplot allows you to search for Trends

Strong Positive Correlation: - strong trend, LOB has a positive slope Weak Positive Correlation - not a strong trend, LOB has a positive slope

Negative Correlation: - The LOB has a negative slope.

A correlation coefficient is a number between -1 and +1 which measures the degree to which two variables are linearly related.

The closer the value is to 1.0, the stronger the relationship. The closer the value is to 0.0, the weaker the relationship. Positive and negative just define slope.

For Pearson’s product-moment correlation coefficient, the greek letter rho (r) is used.

Strong Association between Variables Strong-Moderate Association Weak-Moderate Association Strong-Weak Association Weak-Weak Association Little, if any association

If there is perfect linear relationship with positive slope between the two variables, r = 1

If there is a perfect linear relationship with negative slope between the two variables, r = -1.

If r = 0, there is no linear relationship between the variables.

Coefficient of Determination r 2 represents the fraction of variability in y that can be explained by the variability in x. For example, if r 2 = 0.44, this means that 44% of the variation of the dependant variable is due to the variation in the independent variable.

homework Pg 168 1,2,3,5,6 Pg 180 6