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Consider this set of bivariate data: (20, 61), (30, 85), and (40, 96). Calculate the covariance. 350 175 590 310 545

Consider this set of bivariate data: (20, 61), (30, 85), and (40, 96). Calculate the covariance. 350 175 590 310 545

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Bivariate Data Analysis** **Problem Statement:** Consider this set of bivariate data: (20, 61), (30, 85), and (40, 96). Calculate the covariance. **Answer Choices:** - 350 - 175 - 590 - 310 - 545 **Instructions:** To calculate the covariance, follow the steps below: 1. **Compute the Means:** - \( \bar{x} = \frac{20 + 30 + 40}{3} = 30 \) - \( \bar{y} = \frac{61 + 85 + 96}{3} = 80.67 \) (rounded to 2 decimal places) 2. **Calculate Deviations from the Means:** - For \( x \): - \( 20 - 30 = -10 \) - \( 30 - 30 = 0 \) - \( 40 - 30 = 10 \) - For \( y \): - \( 61 - 80.67 = -19.67 \) - \( 85 - 80.67 = 4.33 \) - \( 96 - 80.67 = 15.33 \) (rounded to 2 decimal places) 3. **Multiply Deviations for Each Data Pair:** - \( (-10) \times (-19.67) = 196.7 \) - \( 0 \times 4.33 = 0 \) - \( 10 \times 15.33 = 153.3 \) 4. **Sum the Products of Deviations:** - \( 196.7 + 0 + 153.3 = 350 \) 5. **Calculate the Covariance:** Covariance ( \( \sigma_{xy} \) ) = \( \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n} \) where \( n \) is the number of data pairs. - \( \sigma_{xy} = \frac{350}{3} = 116.67 \) **Explanation of Answer Choices:** Based on the calculation, the answer closest to our computed covariance (considering the options provided) would be 350, 175, 590, 310, and 545
Transcribed Image Text:**Bivariate Data Analysis** **Problem Statement:** Consider this set of bivariate data: (20, 61), (30, 85), and (40, 96). Calculate the covariance. **Answer Choices:** - 350 - 175 - 590 - 310 - 545 **Instructions:** To calculate the covariance, follow the steps below: 1. **Compute the Means:** - \( \bar{x} = \frac{20 + 30 + 40}{3} = 30 \) - \( \bar{y} = \frac{61 + 85 + 96}{3} = 80.67 \) (rounded to 2 decimal places) 2. **Calculate Deviations from the Means:** - For \( x \): - \( 20 - 30 = -10 \) - \( 30 - 30 = 0 \) - \( 40 - 30 = 10 \) - For \( y \): - \( 61 - 80.67 = -19.67 \) - \( 85 - 80.67 = 4.33 \) - \( 96 - 80.67 = 15.33 \) (rounded to 2 decimal places) 3. **Multiply Deviations for Each Data Pair:** - \( (-10) \times (-19.67) = 196.7 \) - \( 0 \times 4.33 = 0 \) - \( 10 \times 15.33 = 153.3 \) 4. **Sum the Products of Deviations:** - \( 196.7 + 0 + 153.3 = 350 \) 5. **Calculate the Covariance:** Covariance ( \( \sigma_{xy} \) ) = \( \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{n} \) where \( n \) is the number of data pairs. - \( \sigma_{xy} = \frac{350}{3} = 116.67 \) **Explanation of Answer Choices:** Based on the calculation, the answer closest to our computed covariance (considering the options provided) would be 350, 175, 590, 310, and 545
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