Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have the following sets of values for $x$ and $y$:

$x$: $0, 1.5, 2.0, 3.0, 5.0$

$y$: $0.00, 0.92, 1.41, 2.60, 5.59$

I am to find a correlation between the two sets of values. A graph of them gets:

enter image description here

and a graph of $log(x)$ and $log(y)$ finds

enter image description here

in other words a straight line. I now have no idea where to go next. I originally tried the model following, realising afterwards how wrong it was:

To find the correlation I tried to find a $y = kx + m$ equation for the graph, using the values I'd found for $log(x)$ and $log(y)$:

$$k_1 = 0.667$$

$$k_2 = 0.663$$

$$k_3 = 0.674$$

In other words, with some margin of error $k$ is around $0.668$.

$$y = kx + m \iff m = y - kx$$

$$m = 0.9555 - 1.0968\times 0.668 = 0.223$$

$$y = 0.668x + 0.223$$

Testing these values for another $x$ and $y$ shows:

$$0.668\times 0.6931 + 0.223 = 0.686$$

where it should have resulted in $0.3436$.

share|improve this question

1 Answer 1

up vote 0 down vote accepted

I figured it out! Leaving the answer here for anyone working on similar problems.

The fact that the graph has a straight line when using logarithms means that $y$ advances exponentially:

$$\log(y) = \log(x) \times k \iff \log(y) = \log(x^k) \iff y = x^k$$

On top of this we have a constant $C$:

$$\log(y) = \log(C) + \log(x^k) \iff \log(y) = \log(C \times x^k) \iff y = C\times x^k$$

We can gather that the $k$ value is $\frac{\Delta \log(y)}{\Delta \log(x)} = \frac{3}{2}$.

$$\log(y) = \log(C \times x^k) \iff y = C\times x^k$$

$$\Rightarrow C = \frac{y}{x^k} = 0.5008 \approx \frac{1}{2}$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.