Question

41. In Best Buy, the following table shows the weekly demand for the camera in one particular market along with the corresponding price. Determine the sample correlation coefficient between the selling price ($) and the demand for this camera. (5 points) Price (x) Demand (y) 302 17 312 20 322 | 16 331 342 351 363 360

Answer 1

First I have solved the correlation using the excel refer the attached picture below

P 302 17 312 20 322 16 331 14 342 13 351 12 363 9 360 100 25.1 335.375 Correlation 0.351

The correlation coefficient= 0.351

Now calculating it manually average of price = 335.375 and demand is 25.1. Then determine the deviation that is xi - (Average of x) similarly for y

Refer the attached picture

(xі-х)^2 | (уi -у)^2 | (хі-х)/(yі-у) (xі-x/yi-у) yi -y хі -х а 302 17 -33.38 -8.13 66.02 271.17 1113.89 312 20 -23.38 546.39 26.27 119.80 -5.13 322 -13.38 9.13 178.89 83.27 122.05 16 331 -4.38 -11.13 19.14 123.77 48.67 14 342 -80.33 13 6.63 43.89 147.02 -12.13 351 12 15.63 -13.13 244.14 172.27 -205.08 363 9 27.63 -16.13 763.14 260.02 -445.45 360 24.63 74.88 606.39 5606.27 1843.80 100 335.375 25.1 3515.88 6484.88 1674.63

Now square the deviation of x as well as of y. Then multiply deviation of x with deviation of y. Use the following formula

(Xi-X)(yi-y) rxy Σ( -) ΣΥ- y2

$\LARGE \rho = \frac{1,674.53}{\sqrt{3,515.88 \times 6,484.88}}$

$\LARGE \rho = 0.3507$

Correlation = 0.35 (Approximately)

So, we can see using excel as well as manually the correlation coefficient is same.

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