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**Unformatted text preview: **Chapter 9 - Correlation and Regression Section 9.1 - Correlation Objectives • Introduce linear correlation, independent and dependent variables, and the types of correlation • Find a correlation coefficient • Test a population correlation coefficient ρ using a table • Perform a hypothesis test for a population correlation coefficient ρ • Distinguish between correlation and causation Correlation • A relationship between two variables. • The data can be represented by ordered pairs ( x , y ) → x is the independent (or explanatory) variable → y is the dependent (or response) variable Types of correlation: Negative Linear Positive Linear Nonlinear No Correlation Try It Yourself 1 - (p. 497) A sociologist conducts a study to determine whether there is a relationship between family income level and percent of income donated to charities. The data are in the table below. Display the data in a scatter plot and determine the type of correlation. a. Draw and label the x & y axes. b. Plot each ordered pair. c. Does there appear to be a linear correlation? If so, interpret the correlation in context of the data. Income (1,000s) 50 65 48 42 59 72 Donating % 8 6 10 9 5 3 Try It Yourself 2 - (p. 498) A marketing manager conducts a study to determine whether there is a linear relationship between a person's age and the number of magazines to which that person subscribes. The data are in the table below. Display the data in a scatter plot and determine the type of correlation. a. Draw and label the x & y axes. b. Plot each ordered pair. c. Does there appear to be a linear correlation? If so, interpret the correlation in context of the data. Age, x 55 48 26 21 33 50 64 35 Subscriptions, y 2 3 4 3 6 1 Try It Yourself 3 - (p. 498) {alternate} Use TI-83/84 & Excel To do TIY # 1&2 OR do Example 1 p. 497 with Technology. Display the data in a scatter plot and determine the type of correlation. a. Draw and label the x & y axes. b. Plot each ordered pair. c. Does there appear to be a linear correlation? If so, interpret the correlation in context of the data. ($ in thousands) Ad Expenses, x 2.4 1.6 2.0 2.6 1.4 1.6 2.0 2.2 Sales, y 225 184 220 240 180 184 186 215 Correlation coefficient • A measure of the strength and the direction of a linear relationship between two variables. (+/- correlation). • The symbol r represents the sample correlation coefficient. • A formula for r is: • The population correlation coefficient is represented by ρ (rho). • The range of the correlation coefficient is -1 to 1. r = -1 perfect negative correlation, r = 1 perfect positive correlation....

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