Given a data set, and we're tasked with creating a scatter plot and then determining the correlation coefficient PR value. So this scatter plot was created using Excel and Excel has a nice feature that it can. With just a few clicks of the mouse, you can add a trendline. That's this blue dash line right here, and furthermore, you have the option of deciding which shape you would like. So with another quick or two of the mouse, you have the option of displaying the R squared value on the chart, and you also have the option of displaying the equation.įor example, in this case, it's actually literally a line, but you can also choose to try a quadratic or a cubic or a different, uh, degree polynomial. So to determine, are we need to take the square root of R squared, and we need to determine whether it's gonna end up positive or negative. Why increases? Another way to look at that is, is it's sloping upward or downward. Why is increasing as X increases so we're going to take the square root of our square. And of course, we didn't have to calculate to notice that we can see here. The state is not a line it it actually changes direction and trends downward, and then later it trends back upward. It doesn't look anything like the line, so let's try a few other shapes. Let's see what happens if we try and X squared or a parabola. So in this case, here we have our our parabola and r R squared got significantly better. It became 0.923 and we can see it's a pretty decent fit. Uh, the points don't all lie on the curve. In fact, few of them do, but they're fairly close.

This ones maybe a good bit away and this one, but the rest of them are quite near the curb, so it's not surprising we have a decent fit. Let's have a look at what happens if you raise the degree of the polynomial to three. You have a cubic Well, this one isn't even better fit noticed this points a little closer, this one still maintaining its distance about the same, um as is this one. But at least this one got a little closer. So we would expect that the R squared is just a little better. Now let's see what happens if we take it up another degree. Now we have, ah, quite a bit better fit because we're at a degree for we have just a little bit more curvature. And so all of the points are quite close.

In our our skirt is 0.982 So that's looking pretty decent about natural log. So we wouldn't even consider for a moment using natural log for this. Natural law doesn't change directions like that.

Similarly, with the power that a power best fit Excel gave up on it, couldn't even didn't even want to try, which makes sense, because with the power function, um, you wouldn't be able to switch from a positive to a negative, and vice versa.

Excel trendline equation more decimals