Correlation & regression (3)

283 views

Published on

Correlation & regression - Unitedworld School of Business

Published in: Education, Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
283
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
10
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Correlation & regression (3)

  1. 1. Correlation-Regression
  2. 2. It deals with association between two or more variables Correlation analysis deals with covariation between two or more variables Types 1. Positive or negative Simple or multiple Linear or non-linear
  3. 3. Methods of Measuring correlation 1. Graphic Method 2. Diagramatic Method- Scatter Diagram 3. Algebraic method a. Karl Pearson’s Coefficient of correlation b. Spearman’s Rank Co-efficient Correlation c. Coefficient of Concurrent deviations d. Least Squares Method
  4. 4. Karl Pearson’s Coefficient of Correlation Σ dx dy γ ( Gamma) = ------------------------- √ Σ dx2 Σ dy2 Σ dx dy = ------------------------- N σxσy dx = x-xbar dy = y- ybar dx dy = sum of products of deviations from respective arithmetic means of both series
  5. 5. Karl Pearson’s Coefficient of Correlation After calculating assumed or working mean Ax & Ay Σ dx dy – (Σ dx) *( Σ dy) γ ( Gamma) = -------------------------------- √ [ NΣ dx2 - (Σ dx)2 * [Σ Ndy2 - (Σ dy)2 ] Σ dx dy = total of products of deviation from assumed means of x and y series Σ dx = total of deviations of x series Σ dy = total of deviations of y series Σ dx2 = total of squared deviations of x series Σ dy2 = total of squared deviations of y series N= No. of items ( no. of paired items
  6. 6. Karl Pearson’s Coefficient of Correlation After calculating assumed or working mean Ax & Ay Σ dx x Σ dy Σ dx dy - ---------------- N γ ( Gamma) = ------------------------- (Σ dx)2 (Σ dy)2 √ [ Σ dx2 - --------- ] x [ Σ dy2 - ------------] N N
  7. 7. Assumptions of Karl Pearson’s Coefficient of Correlation 1. Linear relationship exists between the variables Properties of Karl Pearson’s Coefficient of Correlation 1.value lies between +1 & - 1 2.Zero means no correlation 3.γ ( Gamma) = √ bxy X byx Where bxy X byx are regression coefficicent Merit Convenient for accurate interpretation as it gives degree & direction of relationship between two variables
  8. 8. Limitations 1. Assumes linear relationship , even though it may not be 2. Method & process of calculation is difficult & time consuming 3. Affected by extreme values in distribution
  9. 9. Probable Error of Karl Pearson’s Coefficient of Correlation 1- γ2 Probable Error of γ ( Gamma) = 0.6745 -------- √ N
  10. 10. Q7.Calculate coefficient of correlation for following data X 65 63 67 64 68 62 70 66 68 67 69 71 Y 68 66 68 65 69 66 68 65 71 67 68 70 Ans Σ dx dy γ ( Gamma) = ------------------------- √ Σ dx2 Σ dy2 Σ dx dy = ------------------- N σxσy
  11. 11. 1 2 3 4 5 6 7 8 9 10 11 12 Su mX Xbar X 65 63 67 64 68 62 70 66 68 67 69 71 800 66.67 Y 68 66 68 65 69 66 68 65 71 67 68 70 811 67.58 dx=x-xbar -1.67 -3.67 0.33 -2.67 1.33 -4.67 3.33 -0.67 1.33 0.33 2.33 4.33 dx2 2.78 13.44 0.11 7.11 1.78 21.78 11.11 0.44 1.78 0.11 5.44 18.78 84. 67 dx.dy -0.69 5.81 0.14 6.89 1.89 7.39 1.39 1.72 4.56 -0.19 0.97 10.47 40. 33 dy=y-ybar 0.42 -1.58 0.42 -2.58 1.42 -1.58 0.42 -2.58 3.42 -0.58 0.42 2.42 dy2 0.17 2.51 0.17 6.67 2.01 2.51 0.17 6.67 11.67 0.34 0.17 5.84 38. 92 Σ dx dy sum dx2* sumdy2 3294. 9 √ Σ dx2 Σ dy2 57.40 coeff of correlation = 0.70
  12. 12. Q8. following information about age of husbands & wives. Find correlation coefficient Husband 23 27 28 29 30 31 33 35 36 39 Wife 18 22 23 24 25 26 28 29 30 32 γ ( Gamma) =0.99
  13. 13. 1 2 3 4 5 6 7 8 9 10 Sum X Xbar X 23 27 28 29 30 31 33 35 36 39 311 31.10 Y 18 22 23 24 25 26 28 29 30 32 257 25.70 dx=x- xbar -8.10 -4.10 -3.10 -2.10 -1.10 -0.10 1.90 3.90 4.90 7.90 dx2 65.61 16.81 9.61 4.41 1.21 0.01 3.61 15.21 24.01 62.41 202. 9 dx.dy 62.37 15.17 8.37 3.57 0.77 -0.03 4.37 12.87 21.07 49.77 178. 3 dy=y- ybar -7.70 -3.70 -2.70 -1.70 -0.70 0.30 2.30 3.30 4.30 6.30 dy2 59.29 13.69 7.29 2.89 0.49 0.09 5.29 10.89 18.49 39.69 158. 1 Σ dx dy sum dx2* sumdy2 32078.4 9 √ Σ dx2 Σ dy2 179.10 coeff of correlation = 1.00
  14. 14. Q9. ten competitors in a cooking competition are ranked by three judges in the following way .by using rank coorelation method find out which pair of judges have nearest approach Ans P&Q= -0.21 , Q &R=--0.3 P &R = +0.64
  15. 15. Q9. ten competitors in a cooking competition are ranked by three judges in the following way .by using rank coorelation method find out which pair of judges have nearest approach P Q R 1 1 3 6 2 6 5 4 3 5 8 9 4 10 4 8 5 3 7 1 6 2 10 2 7 4 2 3 8 9 1 10 9 7 6 5 10 8 9 7
  16. 16. Rank coefficient of correlation 6Σ d2 ρ (rho) = 1 - ------------------- N3 -N Σ d2 = total of squared difference N = number of items
  17. 17. P Q R Rp- Rq dpq2 Rq- Rr dqr2 Rp- Rr dpr2 1 1 3 6 -2 4 -3 9 -5 25 2 6 5 4 1 1 1 1 2 4 3 5 8 9 -3 9 -1 1 -4 16 4 10 4 8 6 36 -4 16 2 4 5 3 7 1 -4 16 6 36 2 4 6 2 10 2 -8 64 8 64 0 0 7 4 2 3 2 4 -1 1 1 1 8 9 1 10 8 64 -9 81 -1 1 9 7 6 5 1 1 1 1 2 4 10 8 9 7 -1 1 2 4 1 1 1000 200 214 0 60 6Sigma d2 1200 1284 360 N3 -N 990 6Sigma d2/N3 -N 1.21 1.297 0.3636 P= -0.21 -0.297 0.636364
  18. 18. Campus Overview 907/A Uvarshad, Gandhinagar Highway, Ahmedabad – 382422. Ahmedabad Kolkata Infinity Benchmark, 10th Floor, Plot G1, Block EP & GP, Sector V, Salt-Lake, Kolkata – 700091. Mumbai Goldline Business Centre Linkway Estate, Next to Chincholi Fire Brigade, Malad (West), Mumbai – 400 064.
  19. 19. Thank You

×