Unit 1 Study Guide Review 2024 Updates

Problem Set 1: Calculate the SD in x and y; covariance; correlation coefficient for the following: 10. Random sample of 7 (x,y) pairs of data points: (1,5)(3,7)(4,6)(5,8)(7,9)(3,6)(5,7) X 11. Random sample of 5 (x,y) pairs of data points: (12,200)(30,600)(15,270)(24,500)(14,210) 12. From the values of x and y in (11), calculate the value of z = x + y for each observation; then calculate z bar. Confirm that z bar = x bar + y bar. {Ans: 10. First find mean of x and y in order to plug into SD formula! -Mean of x = (1+3+4+5+7+3+5)/7 = 4 -Mean of y = (5+7+6+8+9+6+7)/7 = 6.857 --> SD of x = (([(1-4)^2]+[(3-4)^2]+[(4-4)^2]+[(5-4)^2]+[(7-4)^2]+[(3-4)^2]+[(5-4)^2])/6)^(1/2) = *SD of x = 1.915* --> SD of y = (([(5-6.857)^2]+[(7-6.857)^2]+[(6-6.857)^2]+[(8-6.857)^2]+[(9-6.857)^2]+[(6-6.857)^2]+[(7-6.857)^2])/6)^(1/2) = *SD of y = 1.345* --> Covariance = [sum of (x1-mean of x)(y1-mean of y)]/n-1 = measures strength/direction of relationship between x and y data sets --> = ([(1-4)(5-6.857)]+[(3-4)(7-6.857)]+[(4-4)(6-6.857)]+[(5-4)(8-6.857)]+[(7-4)(9-6.857)]+[(3-4)(6-6.857)]+[(5-4)(7-6.857)])/6 = *covariance = 2.333* --> Correlation coefficient = covariance/(SDx*SDy) = shows relationship between data sets (1=strong positive; -1=strong negative; 0=no relationship) = absolute value = relationship strength --> = 2.33/(1.915*1.345) = *correlation coefficient or r = 0.905 = strong positive relationship* 11. First find mean of