Measures of Association Between Two Variables EXAMPLE X xi - x Week Number of Commercials Sales Volume yi- y (xi-x ) (yi- y ) ( xi - x ) 2 (yi-7 ) 2- 3=-1 50- 51= - 1 ( - 1 ) ( - 1 ) = 1 (-1)2 = 1 (-1)2- NN N 8 5 0 5 - 3 = 2 57 - 51 = 6 2 . 6 = 12 6" = 36 1 - 3 = - 2 41- 51= 10 (- 2) ( - 10 ) = 20 (-10) = 100 5 4 3 - 3 = 0 3 4 54 4 - 3 = 1 3 W 3 8 1 - 3 = - 2 GOD JOVIWN 63 - 13 26 (-1 3) 2 5 - 3- 2 48 12 24 59 3 - 3 = 0 4- 3 = 1 - 3 ON WU 46 510 2 - 3 = -1 8 's Total 30 O 20 5bl Sxy = = (xi-x ) (yi- y ) 9 9 = 11 > 0 n - 10 - = ) positive association Mean X = ZXI = 30 = 3 TO 10 y = $10 = 57 man We will use a scatter plo- to isplay association between numerical variables Scatter plot - a graph displaying pairs of values as points on a two dimentional grid. each dot represents INT 70 I ( x , y ) combination . ( + ) 60 I ) xi> x and yi ly 80 III ( xi - x ) ( y - y )> o positive 45 IV III ) xicx and yay 40 ( xi - x )ly . - y ) > o positive positive 35 30 LI and 2 (IV) negative 6 6 reen dot . * i s * = > ( x i - x ) > o yi lyi- y)0 CO negativeECON 15A Homework 3 1. Consider the following data: X 6 7 IN 3 5 UT W 6 7 2 a) Make a scatterplot of these data. The variable labeled "x" should be plotted along the x-axis. Describe the pattern.\f