Understanding r^2 and the Role of Square Root in Data Analysis

[Hammad Shahid]

Hi guys. I was wondering something. In my math class, we were analyzing how strong the data was, and there was an r and r^2 value. I know the significance of r, but what's the point of knowing the square of the r value?

Also, what's the use of square root? Like where does it help? I saw it one time in an equation in my chemistry class (I think Graham's law of effusion/diffusion), and of course, the Pythagorean theorem.

 

[Mark44]

Hi guys. I was wondering something. In my math class, we were analyzing how strong the data was, and there was an r and r^2 value. I know the significance of r, but what's the point of knowing the square of the r value?

I assume you're talking about the correlation coefficient r. I don't know of any significance of r².

Also, what's the use of square root? Like where does it help? I saw it one time in an equation in my chemistry class (I think Graham's law of effusion/diffusion), and of course, the Pythagorean theorem.

The property my house is on is about 100,000 sq. ft. If it were in the shape of a square (which it isn't), what would be the dimensions of this square? (Ans: about 316 ft x 316 ft)

In the equation $E = (1/2)mv^2$, if you know the energy E and the mass m, how would find the velocity v?

The square root let's us solve equations where a variable appears to the second power. Likewise, the cube root let's us solve equations where a variable occurs to the third power.

The square root and cube root are inverse operations to squaring and cubing. When you learn about elementary functions in an algebra or precalculus class, you typically learn about these functions and their inverses.

 

[mjc123]

r² is the fraction of the variance in the y values attributable to the correlation. In other words, if all the points fell on the regression line, the variance in y would be r² * the observed variance. 1-r² is the fraction of the variance attributed to random deviation of the points from the regression line.