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Chapter 3: Examining Relationships

Chapter 3: Examining Relationships. 3.2: Correlation. Measures the direction and strength of a linear relationship between two variables. Usually written as r . Video explaining how r is calculated Fortunately, most of the time we will use our calculators!.

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Chapter 3: Examining Relationships

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  1. Chapter 3: Examining Relationships

  2. 3.2: Correlation • Measures the direction and strength of a linear relationship between two variables. • Usually written as r. • Video explaining how r is calculated • Fortunately, most of the time we will use our calculators!

  3. Example 1 – finding correlation by hand The following data represents the number of absences for 9 different students and their overall grade in the course. Find the correlation.

  4. Important facts about correlation: • Makes no distinction between explanatory and response variables • It doesn’t matter which variable is called x and which is called y • Requires that both variables be quantitative • For example, the correlation between the incomes of a group of people and what city they live in cannot be calculated because city is a categorical variable. • Because ruses standardized values of the observations, it does not change when we change the units of measurement of x, y, or both • r has no unit of measurement; it is just a number. • Positive r indicates positiveassociation and negative r indicates negative association.

  5. Important Facts about correlation: • r is always a number between -1 and 1 • Values near 0 indicate a very weak linear relationship • The strength increases as r moves toward -1 or 1. • Measures the strength of only a linear relationship • Does not describe curved relationships • ris not a resistant measurement • Use r with caution when there are outliers Note: ris not a complete description of two-variable data • Need to use the means and standard deviations of BOTHx and y along with the correlation when describing the data.

  6. Correlation Charts Correlation measures how closely related the data is to a linear approximation. The slope of the correlation gives the sign of the value.

  7. Make a Scatterplot • Use 2nd Y= • Turn plot 1 on • The first type of graph is a scatterplot • Xlist = L1 • Ylist = L2 • Press the zoom key then number 9

  8. Find the Correlation • First, make sure the diagnostics are turned on: • Press 2nd 0 • Brings up catalog • Find DiagnosticOn and press enter twice • Press the STAT key • Scroll over to CALC • Use either option 4 or 8

  9. Example 2 – Using the calculator • Using the data from example 1, find the correlation using your calculator. • STAT/CALC/LinReg • r = -.946

  10. Section 3.2 complete • Homework: p.142-146 #’s 24 (do part a by hand and for part b use lists to find r in your calc), 25, 26, 28, 34, 36, & 37

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