Systolic138 120 130 135 140 ¡100 If you plan to use a 0.05 significance level in
ID: 3065903 • Letter: S
Question
Systolic138 120 130 135 140 ¡100 If you plan to use a 0.05 significance level in a test of correlation between |82 191 100180 Diastolic 1. systolic and diastolic readings, what are the critical values of ? 2. The linear correlation coefficient r is found to be 0.585. What should you conclude? 0.585 and the 3. The sample data result in a linear correlation coefficient of r regression equation y-1.99 + 0.698x. What is the best predicted diastolic reading given a systolic reading of 125, and how was it found? 4. Repeat the preceding exercise assuming that the linear correlation coefficient is r 0.989. 5. Given that the linear correlation coefficient r is found to be 0.585, what is the proportion of the variation in diastolic blood pressure that is explained by the linear relationship between systolic and diastolic blood pressure?Explanation / Answer
Q1.
calculation procedure for correlation
sum of (x) = x = 663
sum of (y) = y = 453
sum of (x^2)= x^2 = 88169
sum of (y^2)= y^2 = 41405
sum of (x*y)= x*y = 60246
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 60246 - [ 5 * (663/5) * (453/5) ]/5- 1
= 35.64
and now to calculate r( x,y) = 35.64/ (SQRT(1/5*60246-(1/5*663)^2) ) * ( SQRT(1/5*60246-(1/5*453)^2)
=35.64 / (7.144*8.523)
=0.585
Q1.
level of significance, = 0.05
from standard normal table, two tailed t /2 =3.182
since our test is two-tailed
reject Ho, if to < -3.182 OR if to > 3.182
Q2.
value of correlation is =0.585 > 0, we see a postive correlation between systolic, diastolic
Q3.
regression equation, y = -1.99 + 0.698x
and the predicted diastolic reading when given a sustolic reading of 125,
=> y = -1.99 + 0.698 * 125
=> y = 85.26
Q4.
when r = 0.989, we call it as perfect positive correlation between the given summarized data
( X) ( Y) X^2 Y^2 X*Y 138 82 19044 6724 11316 130 91 16900 8281 11830 135 100 18225 10000 13500 140 100 19600 10000 14000 120 80 14400 6400 9600Related Questions
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