stats 2 week 9

# stats 2 week 9 - 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 5 10 15...

This preview shows pages 1–3. Sign up to view the full content.

Sarah Anderson Stats 2 Week 9 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. d) The coefficient of determination r^2 is, well, r^2. Zero is uncorrelated, one is perfectly correlated.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 5 10 15 20 25 30 35 40 45 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...
View Full Document

## 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.

### Page1 / 3

stats 2 week 9 - 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 5 10 15...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online