Question

Click here to view the data set. Click here to view the critical values table. i Data set o LLLL 10 10 x y 2 4 4 8 6 10 6 13 7 19 (b) By hand, compute the correlation coefficient. The correlation coefficient is r= (Round to three decimal places as needed.) Print Done (c) Determine whether there is a linear relation between x and y. Because the correlation coefficient is and the absolute value of the correlation coefficient, is than the critical value for this data set, linear relation exists between x and positive not greater greater no negative a negative a positive

Answer 1

TABLE FOR THE COMPUTATION OF CORRELATION CO-EFFICIENT :- xy 32 EX NToot 18 1 - 10 36 100 6 13 36 169 7 19 49 361 133 TOTAL 25 54 141 710 311 :0= Cornelation co-efficient between X and Y = nĘ Xi Yi — (Ixi)CZY) = 5x311- (25xsu) Jn I xiz- (I xi)-In ÇY; 2-([41]? 15x141-(25)[5x710–1542 = 205 ranura = 0.91026 ~ 0.910 (Round to three decimal places in the correlation co-efficient is 0.910 To testhi P (population correlation) = 0 vsk:P #o che mest linea i. The test statistic =1mm-2 - 10.910 x 3 = 3,801 I si-n2 l 1 -0.912 | Considering a = 0.05, Toros = To.025 = 3,182 Hene, 3. 801 > To.025 = 3.182, henee, we should aeeept k, le, there does not exist linean nelationship between x andy Z 80 relationshi Because, the correlation coefficient is positive, and the absolute ralue of the correlation coefficient is 3,801 greater than the enitial rame of this dataset, a positive linear relation Letween X and Y.