Adequacy of Linear Regression Models 1 Data Therm

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Adequacy of Linear Regression Models 1

Adequacy of Linear Regression Models 1

Data

Data

Therm exp coeff vs temperature T α T 80 6. 47 -140 4. 91

Therm exp coeff vs temperature T α T 80 6. 47 -140 4. 91 60 6. 36 -160 4. 72 40 6. 24 -180 4. 52 20 6. 12 -200 4. 30 0 6. 00 -220 4. 08 -20 5. 86 -240 3. 83 -40 5. 2 -260 3. 58 -60 5. 58 -280 3. 33 -80 5. 43 -300 3. 07 -100 5. 28 -320 2. 76 -120 5. 09 -340 2. 45 α T is in o. F; α is in μin/in/o. F Is this adequate?

Quality of Fitted Data Does the model describe the data adequately? How well does

Quality of Fitted Data Does the model describe the data adequately? How well does the model predict the response variable predictably?

Linear Regression Models Limit our discussion to adequacy of straight-line regression models

Linear Regression Models Limit our discussion to adequacy of straight-line regression models

Four checks Does the model look like it explains the data? 2. Do 95%

Four checks Does the model look like it explains the data? 2. Do 95% of the residuals fall with ± 2 standard error of estimate? 3. Is the coefficient of determination acceptable? 4. Does the model meet the assumption of random errors? 1.

Check 1: Plot Model and Data T α T 80 6. 47 -140 4.

Check 1: Plot Model and Data T α T 80 6. 47 -140 4. 91 60 6. 36 -160 4. 72 40 6. 24 -180 4. 52 20 6. 12 -200 4. 30 0 6. 00 -220 4. 08 -20 5. 86 -240 3. 83 -40 5. 2 -260 3. 58 -60 5. 58 -280 3. 33 -80 5. 43 -300 3. 07 -100 5. 28 -320 2. 76 -120 5. 09 -340 2. 45 α

Check 2: Using Standard Error of Estimate

Check 2: Using Standard Error of Estimate

Check 3: Using Coefficient of Determination

Check 3: Using Coefficient of Determination

Check 4. Does the model meet assumption of random errors? Residuals are negative as

Check 4. Does the model meet assumption of random errors? Residuals are negative as well as positive b) Variation of residuals as a function of the independent variable is random c) Residuals follow a normal distribution d) There is no autocorrelation between the data points. a)

a) Are residuals negative and positive?

a) Are residuals negative and positive?

b) Is variation of residuals as a function of independent variable random?

b) Is variation of residuals as a function of independent variable random?

c) Do the residuals follow normal distribution?

c) Do the residuals follow normal distribution?

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What polynomial model to choose if one needs to be chosen?

What polynomial model to choose if one needs to be chosen?

Which model to choose?

Which model to choose?

Optimum Polynomial: Wrong Criterion Both graphs above are same Left one starts at m=1

Optimum Polynomial: Wrong Criterion Both graphs above are same Left one starts at m=1 Right one starts at m=2

Optimum Polynomial: Correct Criterion Both graphs are same Left one starts at m=1 Right

Optimum Polynomial: Correct Criterion Both graphs are same Left one starts at m=1 Right one starts at m=2

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Effect of an Outlier

Effect of an Outlier

Effect of Outlier

Effect of Outlier

Effect of Outlier

Effect of Outlier

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Final Exam Grades 100 Final Exam Grade 90 80 70 60 50 40 0

Final Exam Grades 100 Final Exam Grade 90 80 70 60 50 40 0 10 20 30 Student No 40 50 60

Final Exam Grade vs Pre-Req GPA R 2 = 0, 2227 100 FInal Exam

Final Exam Grade vs Pre-Req GPA R 2 = 0, 2227 100 FInal Exam Scores 90 80 70 60 50 40 1 2 3 Pre-Requisite GPA 4 5

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