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Exam Feb 28: sets 1,2

Exam Feb 28: sets 1,2. Set 2 due today. (1)multiple regression. (a) forecast = 85 -.05(180) + .76(10) -.10(120) +2(1) = 74

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Exam Feb 28: sets 1,2

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  1. Exam Feb 28: sets 1,2 • Set 2 due today

  2. (1)multiple regression • (a) forecast = 85 -.05(180) + .76(10) -.10(120) +2(1) = 74 • (b) If cholesterol incr by 1, age at death decr by .05. If extra minute of exercise, age at death incr by .76. If weight incr by 1 pound, age at death decr by .1. A woman’s life expectancy is 2 years longer than a man’s, all other things equal.

  3. (2) ANOVA • Ho: All 3 population means are = • H1: Not all 3 means = • Sample sizes: n1=n2=n3=3, n = 9

  4. Sample means

  5. Grand mean = 30+12+12 = 6 9 If Ho were true, then we would expect each sample mean to be 6.

  6. SSB = explained variation • SSB = 3(10-6)2+3(4-6)2 +3(4-6)2 = 72 • MSB = SSB/2 = 72/2 = 36

  7. SSW= unexplained variation • (9-10)^2+(10-10)^2+(11-10)^2 +(1-4)^2 + (6-4)^2 + (5-4)^2 +(2-4)^2 + (4-4)^2 + (6-4)^2 = 24 • MSW = SSW/(n-3) = 24/6 = 4

  8. SAM F = MSB/MSW • SAM F = 36/4 = 9 • Critical F • Col 2 • Row n-3 = 9-3 = 6 • CR F = 5.14 • Reject Ho; differences ARE significant since 9>5.14

  9. Regression Dependent variable:Y=mpg Independent variables: X1= wt,X2=cyl,X3=size

  10. Y=48.6-5X1-X2-3.3X3 • (b)If wt incr by 1 ton, mpg decr by 5 (for cars with same cylinders and engine size) • If # cylinders incr by 1, mpg decr by 1 (for cars with same wt and engine size) • If # liters incr by 1, mpg decr by 3.3 (for cars with same wt and cylinders)

  11. (c)Y=48.6-5(2)-6-3.3(3.2)=22 • (d) Actual mileage is typically 1.32 mpg away from expected mpg

  12. (e) 95% of total variation in mpg explained by wt, cyl, size • (f) Ho: NO relationship between all the independent variables and mileage • H1: There IS a relationship between mpg and independent variables • Significance F = p-value =.000265 < .05 • Reject Ho since p-value<alpha • There IS a relationship

  13. Classical stat vs Excel • Classical: Reject Ho if sample F > critical F • Example: ANOVA • Excel: Reject Ho if p-value< alpha • Example: Multiple Regression

  14. (g) • (1) Ho: weight not important to predict mpg H1: weight IS important p-value = .029289 < .05, Reject Ho Weight IS important (2) Ho: Number of cylinders not important H1: Number of cylinders IS important p-value = .1996 > .05, do NOT reject Ho; Cylinders NOT important

  15. (g) • (3) Ho: Engine size NOT important H1: Size matters p-value = .13869 > .05, do NOT reject Ho, engine size NOT important • Only weight is important

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