Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. a. here is a bivariate data set. x y 25.7 5

A. Here is a bivariate data set. x y 25.7 52.5 29.4 64.7 21.8 54.9 35 63.4 31.4 74.7 21.6 46.5 40.8 69.7 37.9 77.7 16.7 41.1 29.6 78.1 13.1 45.5 36.1 78.4 32.1 68.2 45.2 76.8 36.1 57.9 Find the correlation coefficient and report it accurate to...

Free

50.1K

Verified Solution

Question

Basic Math

A. Here is a bivariate data set.

xy
25.752.5
29.464.7
21.854.9
3563.4
31.474.7
21.646.5
40.869.7
37.977.7
16.741.1
29.678.1
13.145.5
36.178.4
32.168.2
45.276.8
36.157.9

Find the correlation coefficient and report it accurate to threedecimal places.
r =
What proportion of the variation in y can be explained bythe variation in the values of x? Report answer as apercentage accurate to one decimal place.
r² = %

B. Based on the data shown below, calculate the correlationcoefficient (to three decimal places)

xy
14.97
24.04
33.51
43.78
55.15
67.22
76.69
85.76
96.73
106.6
119.77
128.24
136.91

Answer & Explanation Solved by verified expert
4.5 Ratings (834 Votes)

Ans:

a)

x y xy x^2 y^2
1 25.7 52.5 1349.25 660.49 2756.25
2 29.4 64.7 1902.18 864.36 4186.09
3 21.8 54.9 1196.82 475.24 3014.01
4 35 63.4 2219 1225 4019.56
5 31.4 74.7 2345.58 985.96 5580.09
6 21.6 46.5 1004.4 466.56 2162.25
7 40.8 69.7 2843.76 1664.64 4858.09
8 37.9 77.7 2944.83 1436.41 6037.29
9 16.7 41.1 686.37 278.89 1689.21
10 29.6 78.1 2311.76 876.16 6099.61
11 13.1 45.5 596.05 171.61 2070.25
12 36.1 78.4 2830.24 1303.21 6146.56
13 32.1 68.2 2189.22 1030.41 4651.24
14 45.2 76.8 3471.36 2043.04 5898.24
15 36.1 57.9 2090.19 1303.21 3352.41
Total 452.5 950.1 29981.01 14785.19 62521.15

Correlation coefficient,r=(15*29981.01-452.5*950.1)/SQRT((15*14785.19-452.5^2)*(15*62521.15-950.1^2))

r=0.810

r^2=0.810^2=0.656 or 65.6%

b)

x y xy x^2 y^2
1 1 4.97 4.97 1 24.7009
2 2 4.04 8.08 4 16.3216
3 3 3.51 10.53 9 12.3201
4 4 3.78 15.12 16 14.2884
5 5 5.15 25.75 25 26.5225
6 6 7.22 43.32 36 52.1284
7 7 6.69 46.83 49 44.7561
8 8 5.76 46.08 64 33.1776
9 9 6.73 60.57 81 45.2929
10 10 6.6 66 100 43.56
11 11 9.77 107.47 121 95.4529
12 12 8.24 98.88 144 67.8976
13 13 6.91 89.83 169 47.7481
Total 91 79.37 623.43 819 524.1671

correlation coefficient,r=(13*623.43-91*79.37)/SQRT((13*819-91^2)*(13*524.1671-79.37^2))

r=0.799
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students