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Type II Error

Type II Error. The probability of making a Type II error is denoted as b . The actual value of b is unknown, we can only calculate possible values for b . Type II Error.

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Type II Error

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  1. Type II Error The probability of making a Type II error is denoted as b. The actual value of b is unknown, we can only calculate possible values for b.

  2. Type II Error Assume we are trying to test to see if the average number of gallons purchased when a driver fills up their tank has fallen. In the past it was 10 gallons and the standard deviation was 4 gallons. A sample of 100 sales is drawn. Set a at .025.

  3. Hypothesis Test with s Known H0: m>10 Ha: m < 10 Reject H0 if: z < -1.96 Alternatively: Reject H0 if:

  4. Type II Error What if m really was 8.5? z = (9.216-8.5)/.4 = 1.79 b = P(z > 1.79) = .0367 What if m really was 9? z = (9.216-9)/.4 = .54 b = P(z > .54) = .2946 What if m really was 9.5? z = (9.216-9.5)/.4 = -.71 b = P(z > -.71) = .7611

  5. Type II Error P. 371-374 Non-graded homework: P. 374, #46, 48

  6. Chapter 14 Simple Linear Regression Model

  7. Regression Used to estimate how much one variable changes with a change in another variable. Carl Friedrich Gaus

  8. Regression Dependent variable – The variable whose behavior we are trying to predict. Independent variable – The variable used to predict the dependent variable.

  9. Temperature and Natural Gas Usage at the Porter Household

  10. Regression Simple Linear Regression Model y = b0 + b1x + e Simple Linear Regression Equation y = b0 + b1x Estimated Simple Linear Regression Equation

  11. Least Squares Criterion

  12. Excel Regression Output

  13. Interpreting the Output b0 – If the average daily temperature is 0 degrees Fahrenheit the predicted gas usage is 45.88 thousand cubic feet b1 – A 1 degree increase in the average daily temperature reduces the predicted gas usage by 0.66 thousand cubic feet over a month

  14. Interpreting the Output What is the predicted natural gas usage if the temperature is 10 degrees? 45.88 – (10)(0.66) = 39.28 What if the temperature is 50 degrees? 45.88 – (50)(0.66) = 12.88 What if the temperature is -10 degrees? 45.88 – (-10)(0.66) = 52.48 What if the temperature is 100 degrees? 45.88 – (100)(0.66) = -20.12

  15. Computing b0 and b1, Example

  16. Computing b0 and b1, Example

  17. Coefficient of Determination The portion of the variation in the data explained by the regression model

  18. Total Sum of Squares The measure of the total variation in the data.

  19. Sum of Squares Due to Regression The measure of the variation explained by the regression line.

  20. Sum of Squares Due to Error The measure of the variation left unexplained by the regression line.

  21. Total Sum of Squares The total sum of squares equals the sum of squares due to regression plus the sum of squares due to error. SST = SSR + SSE

  22. Coefficient of Determinination The share of the variation explained by the regression line. r2 = SSR/SST

  23. Excel Regression Output 3363.7/3696.8 = 0.9099

  24. Sample Correlation Coefficient

  25. Coefficient of Determination

  26. Model Assumptions The error term e is a random variable with an expected value of 0 The variance of e is the same for all values of x. The values of e are independent The error term e is a normally distributed random variable

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