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Stat 1301 More on Regression. Outline of Lecture. 1. Regression Effect and Regression Fallacy 2. Regression Line as Least Squares Line 3. Extrapolation 4. Multiple Regression. 1. Regression Effect and Regression Fallacy. Test - Retest Situation. - PowerPoint PPT Presentation
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Stat 1301Stat 1301
More on RegressionMore on Regression
Outline of LectureOutline of Lecture
1. Regression Effect and Regression Fallacy1. Regression Effect and Regression Fallacy
2. Regression Line as Least Squares Line2. Regression Line as Least Squares Line
3. Extrapolation3. Extrapolation
4. Multiple Regression4. Multiple Regression
1. Regression Effect and 1. Regression Effect and Regression FallacyRegression Fallacy
Hypothetical Grades for the First Hypothetical Grades for the First 2 Tests in a Class of STAT 13012 Tests in a Class of STAT 1301
AVGx = 75 SDx = 10 (Test 1)
AVGy = 75 SDy = 10 (Test 2)
r = 0.7
Test - Retest Situation
Predict the score on Test 2 for a Predict the score on Test 2 for a student whose Test 1 score student whose Test 1 score was...was...
(a) 95(a) 95
(b) 60(b) 60
Regression Line:
Y = .7X + 22.5^
Test-retest situation:
- Bottom group on Test 1 does better - Bottom group on Test 1 does better onon Test 2 Test 2
- Top group on Test 1 falls back on Test - Top group on Test 1 falls back on Test 22The Regression FallacyThe Regression Fallacy
attributing the regression effect toattributing the regression effect to something besides natural spread something besides natural spread around the line. around the line.
The Regression EffectThe Regression Effect
Regression Effect - Regression Effect - ExplanationExplanation
Students scoring 95 on Test 1Students scoring 95 on Test 13 categories3 categories
(a)(a) Students who will average 95 for the course Students who will average 95 for the course(b)(b) Great students having a bad day Great students having a bad day(c)(c) “Pretty good” students having a good day “Pretty good” students having a good day
- There are more students in category - There are more students in category (c)(c) than in than in (b)(b)- Thus, we expect the “average” performance for - Thus, we expect the “average” performance for
those who scored 95 on Test 1 to dropthose who scored 95 on Test 1 to drop
Regression Effect - Regression Effect - ExamplesExamples
4-yr-olds with IQ’s of 120 typically have adult IQ’s around 110.
4-yr-olds with IQ’s of 70 typically have adult IQ’s around 85.
Of major league baseball teams with winning records, typically 2/3 win fewer games the next year.
Note:Note:
The regression effect does not The regression effect does not explain a change in averagesexplain a change in averages
If If rr > 0: > 0: if X is above AVGx, then the predicted Y if X is above AVGx, then the predicted Y
must be above AVGymust be above AVGy
if X is below AVGx, then theif X is below AVGx, then the predicted Y must be below AVGy predicted Y must be below AVGy
2. Regression Line as 2. Regression Line as Least Squares LineLeast Squares Line
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What line is “closest” to What line is “closest” to the points ?the points ?
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• The regression line has smallest RMS size of deviations from points to the line.
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• The regression line has smallest RMS size of deviations from points to the line.
• The regression line is also called the least squares line.
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3. Extrapolation3. Extrapolation
Predicting beyond the range of Predicting beyond the range of predictor variablespredictor variables
3. Extrapolation3. Extrapolation
Predicting beyond the range of Predicting beyond the range of predictor variablespredictor variables
NOT a good idea NOT a good idea
4. Multiple Regression4. Multiple Regression Using more than one independent Using more than one independent
variable to predict dependent variable to predict dependent variable.variable.
Example:Example:
PredictPredict Y = son’s heightY = son’s height
UsingUsing XX11= father’s height= father’s height
XX22= mother’s height= mother’s height
4. Multiple Regression4. Multiple Regression Using more than one independent Using more than one independent
variable to predict dependent variable to predict dependent variable.variable.
Example:Example:
PredictPredict Y = son’s heightY = son’s height
UsingUsing XX11= father’s height= father’s height
XX22= mother’s height= mother’s height
Equation:Equation: Y = mY = m11XX1 1 + m+ m22XX22 + b + b
