Chapter 10: Regression Think about predicting the sons height from - - PowerPoint PPT Presentation

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Chapter 10: Regression Think about predicting the sons height from - - PowerPoint PPT Presentation

May 12, 2023 275 likes •489 views

Chapter 10: Regression Think about predicting the sons height from the fathers height The SD line the SD line the regression line The regression line is used to predict the y variable when we know the x variable. The regression line:

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Chapter 10: Regression

The SD line

Think about predicting the son’s height from the father’s height

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the SD line the regression line

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The regression line is used to predict the y variable when we know the x variable. The regression line:

  • goes through the point of averages (aveX, aveY)
  • with

slope = r (SDY) SDX

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To draw the regression line:

  • go to the point of averages and put a dot
  • move to the right SDX and up r (SDY), put another

dot (if r is negative, move down)

  • join the dots
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Midterm: ave = 75 SD = 10 r = 0.7 Final: ave = 70 SD = 12 Draw the regression line

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To predict or estimate the value of y when you know the value of x:

1.

Find out how many SDs it is above or below the average in the x variable.

2.

Multiply the answer to step 1 by r.

3.

The answer to step 2 tells you how many SDs it is above or below the average in the y variable.

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Example 1. Hanes, men 18-24: average height =70”, SD = 3” average weight = 162lb, SD = 30lb r = 0.47 Approximately what is the average weight of men who are

a)

76” tall?

b)

64” tall?

c)

69” tall?

d)

73” tall?

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Example 2: Midterm: ave = 75 SD = 10 r = 0.7 Final: ave = 70 SD = 12 Estimate the final exam score for someone who got 87 on the midterm

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Example 3: For the men aged 18-24 in the HANES sample, the relationship between height and systolic blood pressure can be summarized as follows: Average height ≈ 70”, SD ≈ 3” Average b.p. ≈ 124mm, SD ≈ 14mm r = -0.2 Estimate the average blood pressure of men who were 6 feet tall.

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Another example: heights and weights

SD line regression line

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CAUTION!

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Example 4: Midterm: ave = 75 SD = 10 r = 0.7 Final: ave = 70 SD = 12

1.

Estimate the final exam score for someone who got 87 on the midterm.

2.

Estimate the midterm score for someone who got 80 on the final.

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There are two regression lines!

Regression line for predicting FINAL Regression line for predicting MIDTERM SD line

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MIDTERM MIDTERM

FINAL

FINAL FINAL

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The Regression Effect

In test-retest situations, people with low scores tend to improve and people with high scores tend to do worse.

WHY? Chance Error!

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The Regression Effect

Observed value = true value + chance error

Example: IQ test scores, average = 100, SD = 15. If someone scores 140 on their first test, they probably got a _________ chance error. If someone scores 80 on their first test, they probably got a _________ chance error.

Positive or negative

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The Regression FALLACY

Attributing the regression effect to something other than chance error.

Example: A group of people get their blood pressure

  • measured. Those that have high blood pressure return and

have their blood pressure measured again. We expect their second measurements to have a smaller average than their first measurements, due to the regression effect. Attributing this apparent drop to a change in behavior is the regression fallacy.