Choose one of the following values of r for each example below. (-1, -.7, 0, .7,
ID: 3234820 • Letter: C
Question
Choose one of the following values of r for each example below. (-1, -.7, 0, .7, 1). You may use some values more than once and you may not use them all. For full credit choose a value and explain briefly. a) A group of employees all get a 10% cut in their salaries. What is the correlation between their salaries before the cut and after the cut? b) The correlation between weight and belt size for a group of men all the same height. Everyone in a large lecture class flips a coin 100 times and records the results. Then everyone in the class does this again. For parts c)-e) keep these two sets of coin tosses in mind - each student provides one data point. c) The correlation between the number of heads in the first set of 100 tosses and the number of heads in the second set of 100 tosses. d) The correlation between the number of heads in the first set of 100 tosses and the number of tails in the first set of 100 tosses. e) The correlation between the number of heads in the first set of 100 tosses and the number of tails in all 200 tosses.Explanation / Answer
Solution:
a) As there is 10% cut for all group of employee. Hence salary of all employee will be decresed by 10% . Hence as the there is a cut salary decreases by the percentage of cut made in employee salary.
so this is the case of perfect positive correlation because as there is a cut in salary by specific percent, Salary decreses by that particular percentage .Hence for this case
r=1
b)If the height remains same. The increse in weight will increse the width of body or width of waist where belt is tied so. As the weight increases belt of size required willget increse. However this is not necessary that weight gain will directly transform into increse in width of belt tied.
so this is the case of strong positive correlation
Hence r= 0.7
best justify our case
c) Fliping a coin 100 times takes place twicwe. Both of the experiment are independent of each other. Occurance of head or tail in 1st round doesnt effect the occurance of head or tail in 2nd round.
Hence no.of head in first 100 round of tosses are not related to no of head in 2nd 100 round tosses.
Hence r=0
d) In any particular round of tosses
no. of head will be equal to = (100 - no. of tail)
so if there is more number of head comes no of tails will be less.
hence this is the case of negative corelation
so r = -0.7