*65*

**Logarithmic regression** is a type of regression used to model situations where growth or decay accelerates rapidly at first and then slows over time.

For example, the following plot demonstrates an example of logarithmic decay:

For this type of situation, the relationship between a predictor variable and a response variable could be modeled well using logarithmic regression.

The equation of a logarithmic regression model takes the following form:

**y = a + b*ln(x)**

where:

**y:**The response variable**x:**The predictor variable**a, b:**The regression coefficients that describe the relationship betweenÂ*x*and*y*

The following step-by-step example shows how to perform logarithmic regression on a TI-84 calculator for the following dataset:

**Step 1: Enter the Data**

First, we will enter the data values. Press STAT, then press EDIT. Then enter the x-values of the dataset in column L1 and the y-values in column L2:

**Step 2: Fit the Logarithmic Regression Model**

Next, we fill fit the logarithmic regression model.

Press Stat, then scroll over to CALC. Then scroll down to LnReg and press ENTER twice.

The following results will be displayed:

**Step 3: Interpret the Results**

We can use the coefficients in the output to write the following fitted logarithmic regression equation:

**y = 76.21296 â€“ 29.8634 * ln(x)**

We can use this equation to predict the response variable,Â *y*, based on the value of the predictor variable,Â *x*. For example, if *x* = 8, then we would predict that *y* would beÂ **14.11**:

y = 76.21296 â€“ 29.8634 * ln(8) = **14.11**

**Bonus:** Feel free to use this online Logarithmic Regression Calculator to automatically compute the logarithmic regression equation for a given predictor and response variable.

**Additional Resources**

How to Perform Linear Regression on a TI-84 Calculator

How to Perform Quadratic Regression on a TI-84 Calculator

How to Perform Exponential Regression on a TI-84 Calculator

How to Create a Residual Plot on a TI-84 Calculator