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Section 11.1

Section 11.1. Day 2. Recall. Linear model is appropriate for set of data if:. Recall. Linear model is appropriate for set of data if: 1) Conditional means fall near a line. Linear model is appropriate for set of data if: 1) Conditional means fall near a line.

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Section 11.1

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  1. Section 11.1 Day 2

  2. Recall Linear model is appropriate for set of data if:

  3. Recall Linear model is appropriate for set of data if: 1) Conditional means fall near a line

  4. Linear model is appropriate for set of data if: 1) Conditional means fall near a line

  5. Linear model is appropriate for set of data if: 1) Conditional means fall near a line 2) Variability is about the same for each conditional distribution

  6. Linear model is appropriate for set of data if: 1) Conditional means fall near a line 2) Variability is about the same for each conditional distribution

  7. Linear model is appropriate for set of data if: 1) Conditional means fall near a line 2) Variability is about the same for each conditional distribution

  8. Spread in values of x is measured by:

  9. Recall, most of the time the theoretical slope, β1, is _________.

  10. Recall, most of the time the theoretical slope, β1, is unknown.

  11. Recall, most of the time the theoretical slope, β1, is unknown. So, we use ___ to estimate β1.

  12. Recall, most of the time the theoretical slope, β1, is unknown. So, we use b1 to estimate β1.

  13. The slope b1 _____ from sample to sample.

  14. The slope b1varies from sample to sample. Is this variation a good thing or not so good?

  15. The slope b1varies from sample to sample. Is this variation a good thing or not so good? Not so good as the variation affects our predictions.

  16. Recall The slope b1 varies from sample to sample. Bold line is true regression line for the population.

  17. Formula for estimating the standard error of the slope b1.

  18. Formula for estimating the standard error of the slope b1. The smaller the standard error of the slope, the better for us.

  19. Formula for estimating the standard error of the slope b1.

  20. Formula for estimating the standard error of the slope b1. residuals

  21. Formula for estimating the standard error of the slope b1.

  22. Formula for estimating the standard error of the slope b1. SSE

  23. Formula for estimating the standard error of the slope b1.

  24. Formula for estimating the standard error of the slope b1. Spread in the values of x or Variability in the values of x

  25. Key Concept The slope b1 of the regression line variesless from sample to sample when: • Sample size is ______________ • Residuals are _______________ • Values of x are ______________

  26. Key Concept The slope b1 of the regression line variesless from sample to sample when: • Sample size is larger • Residuals are _______________ • Values of x are ______________

  27. Key Concept The slope b1 of the regression line variesless from sample to sample when: • Sample size is larger • Residuals are smaller • Values of x are ______________

  28. Key Concept The slope b1 of the regression line variesless from sample to sample when: • Sample size is larger • Residuals are smaller • Values of x are further apart

  29. Page 750, P5 For each quantity, decide which value will give you the larger variability in b1(assuming all other things remain the same).

  30. Page 750, P5 a. The standard deviation, σ, of the individual response values of y at each value of x: 3 or 5

  31. Page 750, P5 a) 3 or 5, a greater variability in the conditional distributions of y results in a larger value in the numerator of Note: s is estimate of

  32. Page 750, P5 b. The spread of the x-values: 3 or 10

  33. Page 750, P5 b) 3 or 10, a smaller spread in the values of x results in smaller value in the denominator of

  34. Page 750, P5 c. The number of observations, n: 10 or 20

  35. Page 750, P5 c) 10 or 20, because all else being equal, a larger (random) sample size tends to result in less variability in the estimates of parameters

  36. Page 750, P5 d. the true slope, β1: 1 or 3

  37. Page 750, P5 d) The true, or theoretical, slope β1does not matter, everything else being equal.

  38. Page 750, P5 e. the true intercept, βo: 1 or 7

  39. Page 750, P5 e) The true, or theoretical, intercept βodoes not matter because, everything else being equal, all the intercept does is indicate whether one cloud of points is higher or lower than another.

  40. Page 744, D3

  41. Page 744, D3 Plot II will produce regression lines with the smallest variation in slopes because: • the conditional distributions of responses (residuals) have smaller variation than in Plot I and • the x-values have greater spread than in Plot III.

  42. Page 744, D3 Plot I has about twice the variability in x as Plot III but also twice the variability in y. Consequently, the two have roughly the same variation in slopes of the regression line.

  43. If you want a regression equation with the smallest estimated standard error of the slope, which of these lists would you use for the values of the explanatory variable? You may assume that each conditional distribution of y has the same variability.

  44. If you want a regression equation with the smallest estimated standard error of the slope, which of these lists would you use for the values of the explanatory variable? You may assume that each conditional distribution of y has the same variability. A. 5, 10, 15, 20, 25 B. 5, 5, 5, 15, 15, 15, 25, 25, 25 C. 5, 5, 5, 5, 5, 25, 25, 25, 25, 25 D. 5, 5, 10, 10, 15, 15, 20, 20, 25, 25 E. 10, 10, 10, 15, 15, 15, 20, 20, 20

  45. If you want a regression equation with the smallest estimated standard error of the slope, which of these lists would you use for the values of the explanatory variable? You may assume that each conditional distribution of y has the same variability.

  46. x = 15 If you want a regression equation with the smallest estimated standard error of the slope, which of these lists would you use for the values of the explanatory variable? You may assume that each conditional distribution of y has the same variability. A. 5, 10, 15, 20, 25 B. 5, 5, 5, 15, 15, 15, 25, 25, 25 C. 5, 5, 5, 5, 5, 25, 25, 25, 25, 25 D. 5, 5, 10, 10, 15, 15, 20, 20, 25, 25 E. 10, 10, 10, 15, 15, 15, 20, 20, 20

  47. x = 15 If you want a regression equation with the smallest estimated standard error of the slope, which of these lists would you use for the values of the explanatory variable? You may assume that each conditional distribution of y has the same variability. A. 5, 10, 15, 20, 25 B. 5, 5, 5, 15, 15, 15, 25, 25, 25 C. 5, 5, 5, 5, 5, 25, 25, 25, 25, 25 D. 5, 5, 10, 10, 15, 15, 20, 20, 25, 25 E. 10, 10, 10, 15, 15, 15, 20, 20, 20

  48. Page 750, P4

  49. Page 750, P4

  50. Page 750, P4 To find SSE: Enter Sulfate in L1 and Redness in L2. Do LinReg L3 = LResid2 Sum(L3)

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