Outline

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LESSON 22 CORRELATION AND REGRESSION

• Outline
• Correlation and Regression Analysis

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CORRELATION AND REGRESSION

• Correlation measures the strength of relationship
  between X and Y.
• The correlation coefficient r expresses the
  strength of the linear relationship between X and
  Y. A related measure is covariance, COV(X,Y). The
  coefficient of correlation is easier to
  understand as its always between -1 and 1.
• Values near -1 or 1 show strong relationship
• Values near 0 show no relationship
• Values near 1 show strong positive linear
  relationship
• Values near -1 show strong negative linear
  relationship

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CORRELATION AND REGRESSION
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CORRELATION AND REGRESSION
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CORRELATION AND REGRESSION

• Salary and expenses for cultural activities, and
  sports related activities are collected from 100
  households. Data of only 5 households shown below

How are the relationships (linear/non-linear,
positive/negative) between (i) salary and
culture, (ii) salary and sports, and (iii)
sports and culture?
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COV 1094787, r 0.5065 (positive, linear)
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COV -33608, r -0.5201 (negative, linear)
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COV -219026, r -0.08122 (no linear
relationship)
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CORRELATION AND REGRESSION
Example 1 Consider Example 1, Lesson 21 a
chemical engineer investigating the relationship
between weight of final product Y (in pounds) and
volume of raw materials X in gallons. Compute the
sample correlation coefficient.
X Y 14 68 23 105 9
40 17 79 10 51
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CORRELATION AND REGRESSION

X Y XY X2 Y2 14 68 23 105 9
40 17 79 10 51
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READING AND EXERCISES
Lesson 22 Reading Section 4-2 pp.
102-107 Exercises 4-9, 4-10, 4-11