MATH 112 Correlation and Regression

Consider the following cases: 1 As salaries increase, the amount spent on luxury goods also increases. 2 As unemployment increases, the amount spent on luxury goods decreases. 3 There is a relationship between gender and the amount spent on clothes. Math031 - Mathematics in the Modern World 2 Correlation and Regression Correlation is a statistical method used to determine whether a relationship between variables exists. Regression is a statistical method used to describe the nature of the relationship between variables, that is, positive or negative, linear or nonlinear. A scatter plot is a graph of the ordered pairs (x, y) of numbers consisting of the independent variable x and the dependent variable y. Math031 - Mathematics in the Modern World 3 Construct a scatter plot for the data on Internet use and Isolation score of high school students. Internet use is measured by the number of hours per week that the students spend on the computer. Isolation is measured by having the students complete a questionnaire. The questionnaire score ranges from 20 to 50, with 50 being the most isolated students. Internet Use Isolation Score 32 45 14 25 23 40 8 25 12 29 Math031 - Mathematics in the Modern World 4 The Correlation coecient measures the strength and direction of a linear relationship between two variables. The range of the correlation coecient is from 1 to + 1. Pearson Correlation Coecient (r) r = n( Pxy) ( Px)(Py) p[n( Px 2) ( Px)2] [n( Py 2) ( Py)2] where n is the number of data pairs. Math031 - Mathematics in the Modern World 5 Example Compute the correlation coecient for the data: Internet Use Isolation Score 32 45 14 25 23 40 8 25 12 29 Math031 - Mathematics in the Modern World 6 When the value of r is near 0, the linear relationship is weak or nonexistent. The closer r to +1 or 1, the more closely the two variables are related. r Descriptive Level ±1.00 Perfect correlation between ±0.75 to ±0.99 High correlation between ±0.51 to ±0.74 Moderately High correlation between ±0.31 to ±0.50 Moderately low correlation between ±0.01 to ±0.30 Low correlation 0.00 No correlation