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Scatter Diagrams

Scatter Diagrams. A scatter plot is a graph that may be used to represent the relationship between two variables. Also referred to as a scatter diagram. Dependent and Independent Variables.

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Scatter Diagrams

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  1. Scatter Diagrams A scatter plot is a graph that may be used to represent the relationship between two variables. Also referred to as a scatter diagram.

  2. Dependent and Independent Variables A dependent variable is the variable to be predicted or explained in a regression model. This variable is assumed to be functionally related to the independent variable.

  3. Dependent and Independent Variables An independent variable is the variable related to the dependent variable in a regression equation. The independent variable is used in a regression model to estimate the value of the dependent variable.

  4. Two Variable Relationships(Figure 11-1) Y X (a) Linear

  5. Two Variable Relationships(Figure 11-1) Y X (b) Linear

  6. Two Variable Relationships(Figure 11-1) Y X (c) Curvilinear

  7. Two Variable Relationships(Figure 11-1) Y X (d) Curvilinear

  8. Two Variable Relationships(Figure 11-1) Y X (e) No Relationship

  9. Correlation The correlation coefficient is a quantitative measure of the strength of the linear relationship between two variables. The correlation ranges from + 1.0 to - 1.0. A correlation of  1.0 indicates a perfect linear relationship, whereas a correlation of 0 indicates no linear relationship.

  10. Correlation SAMPLE CORRELATION COEFFICIENT where: r = Sample correlation coefficient n = Sample size x = Value of the independent variable y = Value of the dependent variable

  11. Correlation(Example 11-1) Correlation between Years and Sales Excel Correlation Output (Figure 11-5)

  12. Correlation TEST STATISTIC FOR CORRELATION where: t = Number of standard deviations r is from 0 r = Simple correlation coefficient n = Sample size

  13. Correlation Significance Test(Example 11-1) Rejection Region  /2 = 0.025 Rejection Region  /2 = 0.025 Since t=4.752 > 2.048, reject H0, there is a significant linear relationship

  14. Correlation Spurious correlation occurs when there is a correlation between two otherwise unrelated variables.

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