# Exploration 2

## Estimating and Using Linear Regression to Calculate Trend Lines

To analyze the Antarctica and Greenland data and estimate the pattern of temperature anomalies, you did a simple calculation to estimate the rate of change for several glacial-interglacial periods. Scientists, however, analyze data using statistical methods.

To get a more accurate understanding of the relationship between two variables (temperature anomalies and time), scientists often use linear regression. Linear regression computes a straight line that is the best fit through the values (temperature anomalies in this case) in such a way that the values’ distances from the line are minimized. A line of best fit or a linear regression line is also called a trend line and can be expressed by the following equation.

y = mx + b

The “m” is the slope and the “b” is the y-intercept (the point on the vertical axis where the line crosses). The slope is a measurement of how steep the line is. The slope of a line is also known as the rate of change. It is calculated by the following equation.

Slope =vertical change (rise)/horizontal change (run) = y2 - y1/ x2 – x1

Throughout the investigation, remember that:
line of best fit = linear regression line = trend line
and
slope = rate of change

***To print this exploration and record your responses, download this PDF document  .***

## Part A - Estimating the Temperature Trend For the Past 125 Years

Often scientists will try to determine the relationship between variables by creating a trend line or line of best fit. This line will have points of data both above and below the line. For this first activity, you will “draw” your own trend line for the data presented.

Use this interactive, time-series graphing tool to answer the following:

1. Click on the Show Slope button.
2. Adjust the slope and the y-intercept by moving the sliders below the graph. Make your best estimate of the slope and location of the trend line.
3. Click on the Take Snapshot button. An image of the graph with your trend line will appear.
4. Right click on the image and save the image to your computer.
5. Insert the image (Insert>Picture) into the student worksheet.
6. What is the slope of this line? (The slope is shown in the bottom left corner.) Round to the nearest one thousandth. _____________________________
7. Based on your estimated slope, what is the average rate of change in temperature anomalies over 100 years? (Hint: Multiply your slope by 100.)

## Part B - Using Linear Regression to Calculate the Temperature Trend For the Past 125 Years

In this exploration, you are going to calculate the slope of the line for different time periods using a simple regression analysis in Microsoft Excel. (NOTE: You will need the separate set of instructions for this activity.) Open the directions and download the data now. Throughout the exploration, you will be asked to enter your results in the table below. Once you have finished this activity in Excel, you can write your answers in the table.

Time Interval
(Years)
Specific Instructions
-Number
Slope of Line of Best Fit
Calculated by Excel Formula
for Regression – SLOPE
(See Instructions 1-5.)
1885-2010 1.k
1910-2010 2.d
1935-2010 3.d
1960-2010 4.d
1985-2010 5.d
Analysis of Findings

1. How does the slope of the recent 25-year trend line generally compare to the slope of the past trend lines?
2. During which time interval was the rate of change in temperature anomaly the highest?