Question

Examine the computation formula for r, the sample correlation coefficient (a) In the formula for r, if we exchange the symbols x and y, do we get a different result or do we get the same (equivalent) result? Explain your answer The result is different because the formula is dependent on the symbols. The result is the same because the formula is dependent on the symbols. The result is the same because the formula is not dependent on the symbols. The result is different because the formula is not dependent on the symbols. ( f we have a set of x and y data values and we exchange corresponding x and y values to get a new data set, should the sample correlation coefficient be the same for both sets of data? Explain your answer. The result is the same because the formula is not dependent on which values are the x values and which values are the y values. The result is different because the formula is dependent on which values are the x values and which values are they values. The result is the same because the formula is dependent on which values are the x values and which values are they values. The result is different because the formula is not dependent on which values are the x values and which values are the y values (c) Compute the sample correlation coefficient for each of the following data sets and show that is the same for both. (Use 3 decimal places.) SS

Answer 1

Sduction.'- (a) The results is the same is met dependent on the because i we get the exact as formula is Symabilies. because the formula. symetes . se is same result (6) The formala. are the the result is different because the is dependent on which values. p values and which values are y values. (© () 16 4 4 Isolt In 16 16 1 | 16 | 16 | 81 Exi= 17 | Eyj = 13 | EX; 19; = 47 &ci= 113 Eyi : 57 Correlation coefficient of Pearson Correlatio is given by :

xy = n Excy - CESC) CEY) in CEZ) - (Ex)2 ) MEY) -(87)2 3x77 - 17X13 J 3x 113 -4772 3x 57 - (1332 231 - 221 ✓ 339 - 289 171 - 169. - 10 _10 10 - 7.071 X 1.414 10 9.9983 = = 1.0002 Correaktion co - efficient in 1.000

ci) 16. 116 Esiz 13 Eyi = 17 Scigiz 77 $a = 57 Esti = 13 by! Caldelation for 1. co-effecient is given ņ Exy -(Ex) (Ey) my In Cest) (Ex)? Jn (8%)-(Ey)2 3 X 77 - 13X 17 √3x 57 - (137 √3x 113 - (17)2 231 - 221 J 172 - 169 V 339 –289. i 10 1.414 X 7.071 _10 9.9983

1.0002 correlation coeffcient, rs 1.0002 The-end