Bivariate inductive statistics - interval variables

Simple linear regression, Pearson's correlation coefficient

Regression Analysis refers to a group of techniques for studying the straight-line relationships among two variables: Y=f(X) . X is called independent (predictor) variable and Y-dependent (response) variable. Although the regression problem may be solved by a number of techniques, the most-used method is least squares. The least squares method seeks for intercept and slope (coefficients of regression function) to minimize the sum of the squared e's (residuals - differences between actual and predicted Y's). Many of assumptions that must be considered when using regression analysis refer to residuals (constant variance of e's for all X's, normality of e's, independence of e's).

Correlation coefficient rho is a popular statistic for describing the strength of the relationship between two variables. The correlation ranges between plus and minus one. R = 0 is no linear correlation, R = 1 is perfect positive linear correlation, R = −1 is perfect negative.

Example: Is product's sale (Y) effected by advertising costs (X) ?
What increase in sales can we expect if we rise advertising costs by $1 mil.?