Statistics Terminology

Correlation and Regression:A correlation exists between two variables when one of them is related tothe other in some way.Assumptions:1) The sample of paired data (x, y) is a random sample.2) The pairs of (x, y) data have a bivariate normal distribution.(each x corresponds with a y to give a normal curve)A scatter plot is a graph in which the paired sample data, (x, y) are plottedwith x as the horizontal axis and y as the vertical axis.Linear Correlation Coefficient:The linear correlation coefficient, r, measures the strength of thelinear relationship between the paired x and y values of a sample.Pearson Product Moment Correlation Coefficientr =nn∑xy− ( ∑ x)( ∑y)222( ∑ x ) − ( ∑ x) n( ∑ y ) − ( ∑ y) 2n = number of pairs of datar = linear correlation coefficient for a sampleρ = linear correlation coefficient for a populationProperties of the Linear Correlation Coefficient:1) The value of r is always between -1 and 1 inclusive.2) The value of r does not change if all the values of eithervariable are converted to a different scale.3) The value of r is not affected by the choice of x or y4) R is this form measures the strength of a linear relationshiponly!Formal Hypothesis TestingUsing Method 1HH01: ρ = 0: ρ ≠ 0linear correlation when ρ ≠ 0