stats 2 week 9

# stats 2 week 9 - 8 t=rsqrt(n-2/sqrt(1-r^2...

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Sarah Anderson Stats 2 Week 9 Exercises 10 (page 466) 2. Number of cases 8 ∑ X = 39 ∑ Y = 85 ∑ X^2 = 211 ∑ Y^2 = 983 ∑ XY = 378 ∑ X ∑ Y = 378 r = ( ∑ XY - ∑X ∑Y / n ) / SQRT { [∑ X^2 - (∑X)^2 / n] [∑ Y^2 - (∑Y)^2 / n]} Numerator of r = (378) - (39)(85) / 8 = -36.375 Denominator of r = SQRT[211 - (39)^2 / 8] * SQRT[983 - (85)^2 / 8] = SQRT[20.875] * SQRT[79.875] r = -36.375 / [4.56892] * [8.93728] Correlation coefficient r = -0.8908 Coefficient of determination = r^2 = (-0.8908)^2 =0.7935 Because r^2=0.7935 , 79.35% of variation in y is explained by x The correlation coefficient is negative. This means as x increases, y decreases and there is a negative association between x and y. 4. a)r={<xy>-<x><y>}/{sqrt(<x^2>-<x>^2)sqrt(<y^2>-<y>^2)} where <x> is the average of x. Here it doesn't matter which column are x-values and which column are y-values b. c. the more assemblers, the more units are assembled. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 5 10 15 20 25 30 35 40 45

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d) The coefficient of determination r^2 is, well, r^2. Zero is uncorrelated, one is perfectly correlated.
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Unformatted text preview: 8. t=rsqrt(n-2)/sqrt(1-r^2) t=(-0.46)sqrt(13)/(1-(-0.46)^2) t=(-0.46)(3.605551)/0.887919 t=-1.8679 With a significance level of 0.05, and 13 degrees of freedom, the critical t for a one-tailed test is -1.771-1.8679<-1.771 Therefore, we reject the null hypothesis and conclude p < 0 10. 14. The 8 x-y pairs are: (5,13); (3,15); (6,7); (3,12); (4,13); (4,11); (6,9); (8,5) The equation for linear regression is given by: y = ax + b where "a" is determined from: a = [(Σxy)N - (Σx)(Σy)]/[(Σx²)N - (Σx)²] and "b" is determined from: b = [(Σx²)(Σy) - (Σx)(Σxy)]/[(Σx²)N - (Σx)²] where: Σx = 39 Σx² = 211 Σy = 85 Σxy = 378 N = 8 Therefore: a = [(378)(8) - (39)(85)]/[(211)(8) - (39)²] = -291/167 = -1.742515 b = [(211)(85) - (39)(378)]/[(211)(8) - (39)²] = 3,193/167 = 19.119760 Thus, the equation is: y = (-1.742515)x + 19.119760 For x = 6: y = (-1.742515)(6) + 19.119760 = 8.665...
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## This note was uploaded on 04/12/2011 for the course STAT 2610 taught by Professor Sanjeev during the Spring '11 term at Bemidji State.

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stats 2 week 9 - 8 t=rsqrt(n-2/sqrt(1-r^2...

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