1. LSP 120: Quantitative Reasoning and Technological Literacy Section 118 Özlem Elgün

2. Linear Modeling-Trendlines The Problem - In the “real world” most data is not perfectly linear. How do we handle this type of data? The Solution - We use trendlines Why - If we find a trendline that is a good fit, we can use the equation to make predictions

3. Five guidelines to see if the trendline a good fit for the data Guideline 1: Do you have at least 7 data points? Guideline 2: Does the R 2 value indicate a relationship? Reminder: R 2 is the percentage of variance of y that is explained by our trendline. It is a standard measure of how well the trendline fits the data. Guideline 3: Verify that your trendline fits the shape of your graph. Guideline 4: Look for outliers Guideline 5: Use practical knowledge/ common sense to evaluate your findings

4. Justifying your prediction in words Once we calculate the answer to the question, we cannot simply report the numbers. We need to present them in meaningful sentences that explain their meaning in their contexts. SAMPLE LEAD SENTENCES “If the trend established from 1967- 1996 persists, we expect the Women’s world record to be ----------- seconds in 1998. “ SUPPORTING SENTENCES “We are confident in our prediction because the r-squared value of ---------- shows that the data has a strong/ moderate/weak linear relationship. Even though in the long term we expect the rate of change in women’s mile records to decrease and not stay constant, we expect that in the very near future the linear trend should continue, giving us confidence in our prediction. ITEMS THAT MIUST BE POINTED OUT WHEN APPLICABLE Reason for using less than 7 data points. Omitting any single data point. Focusing on a localized linear trend. Continuing to predict a higher amount when they trend actually decreases (or the opposite). http://www.olympic.org/en/content/Sports/All-Sports/Athletics/Track/All-Track-events/1500mMen/ I

5. Adding a Trendline (in Excel 2007) Open the file: MileRecordsUpdate.xls and calculate the slope (average rate of change) in column H for Men’s World records in the Mile Run.MileRecordsUpdate.xls Is this men’s data perfectly linear? Can you use a linear model to describe the data? (Hint: Graph the data in a simple scatter plot) Create a graph with a trendline, title your graph appropriately. What would the men’s world record be in the year 2000? (Hint: in your calculations you need to use the SLOPE and INTERCEPT Excel functions, and use the linear equation.) Check you answer by extending the trendline to year 2000. (right click on trendline, under forecast, increase it forward by number of units you need to, to reach 2000). Does your trendline show a similar number as your prediction. Once you calculate your answers write your answers our in meaningful sentences, justifying your prediction in words. (Hint: report your prediction, the R-squared value, and any possible caveats.)