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Scatter Diagrams; Correlation Section 4.1

2. Objectives 4.1. Draw scatter diagramsInterpret scatter diagramsUnderstand the properties of the linear correlation coefficientCompute and interpret the linear correlation coefficient. 3. Variables. Recall from Chapter 1 that the response variable is the variable of interest and the factors tha

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Scatter Diagrams; Correlation Section 4.1

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    1. Scatter Diagrams; Correlation Section 4.1 Alan Craig 770-274-5242 acraig@gpc.edu

    2. 2 Objectives 4.1 Draw scatter diagrams Interpret scatter diagrams Understand the properties of the linear correlation coefficient Compute and interpret the linear correlation coefficient

    3. 3 Variables Recall from Chapter 1 that the response variable is the variable of interest and the factors that affect the response variable are the predictor variables. Lurking variables may also affect the response variable but have not been identified in the study.

    4. 4 Variables Definition The response variable is the variable whose value can be explained by or determined by the value of the predictor variable(s). Lurking variables are related to the response or predictor variables (or both) but are not included in the study

    5. 5 Example: Variables In a study of a number of different automobile models, the weight of the car and the drive ratio of the car were used as variables to predict fuel consumption. Tire inflation pressure can also affect fuel consumption but was not studied. Response variable: fuel consumption Predictor variables: weight of car, drive ratio Lurking variable: tire inflation pressure

    6. 6 Scatter Diagram Definition A graph that shows the relationship between two quantitative variables measured on the same individual. Predictor variable is on the x-axis Response variable is on the y-axis

    7. 7 Scatter Diagrams

    8. 8 Interpreting Scatter Diagrams Positively correlated—if predictor variable increases , so does the response variable . (positive slope) Negatively correlated—if the predictor variable increases , then values of the response variable decrease . (negative slope)

    9. 9 Example, Prob 12 p.157 (Scatter plot done in SPSS) Are the variables positively or negatively correlated?

    10. 10 Example, Prob 12 p.157 (Scatter plot done in calculator) See handout for calculator instructions.

    11. 11 Linear Correlation The linear correlation coefficient measures the strength of the linear relationship between two quantitative variables. r (Greek letter rho) is used for the population correlation coefficient and r for the sample correlation coefficient. It is also called the Pearson product moment correlation coefficient.

    12. 12 Sample Correlation Coefficient

    13. 13 Properties of the Linear Correlation Coefficient -1= r = 1 r = +1 ? perfect positive linear relation r = -1 ? perfect negative linear relation Closer r is to 1 or -1 the stronger the relation (positive or negative) r close to 0, no linear relation Unit of measure of x, y does not matter, r is unitless

    14. 14 Example, Prob 12 (c/d) p.157 (c) Compute the linear correlation coefficient between the number of carats and the price of a diamond. (d) Comment on the type of relation that appears to exist between the number of carats and price. See the handout for calculator instructions.

    15. 15 Example, Prob 12 p.157 r = .9917 In section 4.2/4.3, we will discuss the other items.

    16. 16 Example, Prob 12 (e) p.157 (e) Remove the diamond that weighs 1.18 carats from the data set and recalculate r. What is the effect of removing this data point? Why do you think this happened?

    17. 17 Example, Prob 12 (e) p.157 r = .9707 Less than before. Why?

    18. 18 Questions ???????????????

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