# Natural log's purpose

In reading 13 there is an example, #3 I think, that discusses or explains the sales trend on intel for 20 years worth of data. It showed that regular linear models don’t fit the trend line and they used the log linear and that explained the sales trend perfectly. Can someone explain the log normal function, how do you know when to use it, (besides when regular models don’t fit exactly.)

It’s for graphs that plateau after a while.

Use linear when growth is at a constant AMOUNT Use loglinear when growth is at a constant RATE The latter accounts for compounding.

To expand on the previous post: Suppose a company’s sales grow at 10% a year: 1) 100k 2)110k 3)121k 4)133.1k 5)146.41k Trying to use a linear regression model simply will not work. Our predictions would be based on the assumption that there is a linear relationship amongst our variables which we have defined them not to be. However, by using the Log Linear function, we’re able to convert the pattern into one that is effectively linear, thereby allowing us to use a regression equation to try to explain the future. The reason a Log Linear function works, is because we are essentially removing the exponential and converting it into a coefficient (at least thats how I look at it)

what do you mean converting it into a coefficient

Look at a linear graph which shows sales data from years 1 to 10. * If sales from year 1 to 2, went from \$10 to \$20, that’s a 100% rise, or \$10 rise. * If sales in year 9 to 10 went from \$1000 to \$1010, a rise by \$10, same as before, but that’s only a 1% rise. * A linear graph would show both changes as covering same distance on the graph, i.e., the jump from one year to the next measures the same on the graph. But why so? The first one is a big change (100%), while the other is a smal change (1%). A loglinear graph takes care of that.

nice, thanks!

wait in your example, that is a constant amount, so use linear?

Even if it grows by a constant amount, a loglinear graph shows the growth situation in a much better way. A linear graph is ok to use, and the two become almost the same, when you have a few data points, or the growth rate is very small. I don’t think the statement made above which says: Use linear when growth is at a constant AMOUNT Use loglinear when growth is at a constant RATE … is a correct rule of thumb.