Stat1000W12_A2_sols

Stat1000W12_A2_sols - STAT 1000 Assignment 2 DUE: February...

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Unformatted text preview: STAT 1000 Assignment 2 DUE: February 8th (Wed. Eve. Section), February 9th (T/Th. Sections), February 10th (MWF. Sections) SHOW ALL YOUR WORK 1. [5] Consider the following 10 data points: x 3 5 6 4 3 7 6 5 4 7 y 4 3 2 1 2 3 3 5 4 2 (a) Plot the above observations on a scatterplot. Solution: untitled: Fit Y by X of y by x Page 1 of 1 1 2 3 4 5 y 3 4 5 6 7 x Linear Fit y = 3.4 - 0.1*x RSquare RSquare Adj Root Mean Square Error Mean of Response Observations (or Sum Wgts) 0.015504-0.10756 1.25996 2.9 10 Summary of Fit Model Error C. Total Source 1 8 9 DF 0.200000 12.700000 12.900000 Sum of Squares 0.20000 1.58750 Mean Square 0.1260 F Ratio 0.7318 Prob > F Analysis of Variance Intercept x Term 3.4-0.1 Estimate 1.463942 0.281736 Std Error 2.32-0.35 t Ratio 0.0487* 0.7318 Prob>|t| Parameter Estimates Linear Fit Bivariate Fit of y By x (b) Calculate the correlation coefficient, r ( by hand ). What does this value tell us? Solution: Preliminary Calculations: x = 5 and y = 2 . 9 s x = 1 . 49 and s y = 1 . 20 r = 1 n- 1 n X i =1 x i- x s x y i- y s y = 1 ( n- 1) s x s y n X i =1 ( x i- x ) ( y i- y ) x i- x y i- y ( x i- x )( y i- y ) (3 - 5) = -2 (4 - 2.9) = 1.1-2.2 (5 - 5) = 0 (3 - 2.9) = 0.1 (6 - 5) = 1 (2 - 2.9) = -0.9-0.9 (4 - 5) = -1 (1 - 2.9) = -1.9 1.9 (3 - 5) = -2 (2 - 2.9) = -0.9 1.8 (7 - 5) = 2 (3- 2.9) = 0.1 0.2 (6 - 5) = 1 (3 - 2.9) = 0.1 0.1 (5 - 5) = 0 (5 - 2.9) = 2.1 (4 - 5) = -1 (4 - 2.9) = 1.1-1.1 (7 - 5) = 2 (2 - 2.9) = -0.9-1.8 n i =1 ( x i- x ) ( y i- y ) = -2 Therefore- 2 (9)(1 . 49)(1 . 20) =-0.124 Interpretation: There is weak negative association between x and y . (c) Calculate the least squares regression line. Solution: Preliminary Calculations: x = 5 and y = 2 . 9 s x = 1 . 49 and s y = 1 . 20 and r =- . 124 (from the previous question), if it is used correctly in this part and was wrong in the previous part, no additional marks are deducted. b 1 = r s y s x =- . 124 1 . 20 1 . 49 =- . 10 b = y- b 1 x = 2 . 9- (- . 10)(5) = 3 . 4 Therefore, y = 3 . 4- . 10 x 2. [11] A foods-and-nutrition investigator would like to know if the amount of sodium (g) can be predicted by the amount of sugar (g) in the following sample of 12 popular breakfast cereals. Cereal Sugar (g) Sodium (g) Mini Wheats 7 All-Bran 5 0.26 Apple Jacks 14 0.13 Captain Crunch 12 0.22 Cheerios 1 0.29 Cinnamon Toast Crunch 13 0.21 Corn Flakes 2 0.29 Raisin Bran 12 0.21 Oat Bran 10 0.14 Crispix 3 0.22 Frosted Flakes 11 0.20 Fruit Loops 13 0.13 (a) Identify the response and explanatory variables. Solution: The response variable is the amount of sodium....
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Stat1000W12_A2_sols - STAT 1000 Assignment 2 DUE: February...

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