# How to derive the trendline equation. Equations of trend lines: Phone data

Logarithmic model Power model We will show how to find an equation for a data set, assuming we know what model would be the best one to represent the data.

Best fitting linear curves Link to video of this example For a first example, we are running a widget factory and have the following data on employee performance: A parenthetical note: In economics, widget is a placeholder name for a generic manufactured device. It is only in recent times that it has also become a small computer GUI unit. We would like a formula for widgets produced as a function of hours worked. Since we can see two entries each, for 36, 43, and 44 how to derive the trendline equation worked, there cannot be a function that hits all our data exactly.

While we expect a linear function, we are not surprised if there is random noise, as a worker may take a break, or be particularly focused on a given day.

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We start by creating a scatterplot for my data. We right click control-click on a mac on one of the data points and we get a contextual menu.

We select Add Trendline. When adding a trend line, we need to select from a number of options. The first option concerns the mathematical model we want to choose.

## Trendline coefficients

Given that we suspect the number of widget produced will be roughly proportional to the hours worked, we want to use a linear model, so we make that choice. Under options, we want to display the equation on the chart. We have added a linear trend line to the graph and can also see the equation for the line.

We could use that equation to plan how many hours we want our workers on the binary options news video based on the number of widgets we expect to sell.

Having found a best fitting line, I want to copy the equation back into my spreadsheet and to be able to compare the values in my data with the projections from my equation. You should notice that the equation Excel produces in the chart is written in standard mathematical notation, while the corresponding equation in cell B3 is in Excel notation. In Excel notation we need a symbol for multiplication rather than simply putting a number and variable together.

A linear regression fits the lineor as Excel prefers to call itto the existing data set. It does so through a technique known as minimizing the sum of the squares of the error terms.

In Excel notation, we how to derive the trendline equation use a cell reference, B1, rather than a variable, x. Checking and improving our equations Link to video of this example When finding the best fitting curve to data we have gathered, we need to pay attention to the model we have chosen and to the range to which we want to apply it.

In our example, the linear fit looks pretty good.

### Excel: Calculate a Trendline Forecast

However we should be careful about using it on too wide a domain. According to our model, a worker who works no hours produces The other issue is the choice of a model.

We chose a linear model.

- Excel trendline equation is wrong - reasons and fixes Excel trendline types When adding a trendline in Excel, you have 6 different options to choose from.
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An argument could easily be made for a proportional model. A worker who works no hours produces no widgets. We can switch to the proportional model by setting the y-intercept to 0 in options for the trend line.

In our case, we can get a better fit by allowing the curve to be a 6th degree polynomial. However the resulting equation does not make sense.

## Line of Best Fit (Least Square Method)

It predicts that a worker will produce about quarter million widgets with a 1-hour work week, and widgets with a hour work week. Fitting the Consumer Price Index CPI to a best fitting curve; an extended example Link to video of this example For our second example, we will look at the consumer price index and try and fit it to a model. This example will illustrate several issues we need to keep in mind when building models. The data from to is in the worksheet SectionExamples.

Since we expect prices to rise as a percentage of the current prices, we expect the CPI to be modeled by an exponential curve.

## Using Excel to find best-fit curves

We start by selecting the data, producing a scatterplot, and adding a best fitting curve using an exponential model. We will always select the option to show the equation on the chart. This first attempt gives an exponential formula, but it is unsatisfactory for a number of reasons. That constant only shows one significant digit, which is not enough to make meaningful predictions.

The font size is too small to easily read off the resulting equations.

### Equations of trend lines: Phone data

The constant coefficient is ridiculously small because it gives the projected value of the index in the year 0.

Another way of thinking about this is that the values we are evaluating this exponential function at run in the thousands!. The graph does not look like a very good fit. The plot of the numbers actually looks as though internet investment with profit represents three different graphs.

We will work through the problems one at a time. The first problem is that the equation Excel has given us does not have enough significant digits to make useful predictions.

We are given a dialog box that lets us make formatting options. Since the lead coefficient is so small, we want the numbers formatted in Scientific notation.

We choose 4 digits beyond the decimal point in that notation. This gives us a better equation.

It should be noted that our pictures in this book use the font option in the formatting to use a larger sized font. The next issue to deal with is adjusting the year.