Question

Find the value of the linear correlation coefficient r. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters).
Temp 62 76 50 51 71 46 51 44 79
Growth 36 39 50 13 33 33 17 6 16
A. 0
B. 0.196
C. -0.210
D. 0.256

Answer 1

D. 0.256 is the correct answer

Answer 2

The linear correlation coefficient is number determined from the given data which measure the strength of relationship between two variables.

The value of the linear correlation coefficient r is 0.196.

Given:

In the table the temperature and growth rate are given.

Write the formula to calculate the linear correlation coefficient.

$r_{xy}=\dfrac{n\sum x_iy_i-\left(\sum x_i\right )\left(\sum y_i\right)}{\sqrt{n\left(\sum x_i^2\right )-\left(\sum x_i\right )^2}\sqrt{n\left(\sum x_i^2\right )-\left(\sum x_i\right )^2} } }$

Refer the attached table to substitute the value.

$r_{xy}=\dfrac{9(14615)-(530)(243)}{\sqrt{9(32656)-(530)^2}\sqrt{9(8245)-(243)^2} }\\r_{xy}=0.1955$

Thus, the value of the linear correlation coefficient r is 0.196.

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