1. The slope of a linear association plays the same role as the slope of a line in algebra. Slope is the amount of change we expect in the dependent variable (Δy) when we change the independent variable (Δx) by one unit. When describing the slope of a line of best fit, always acknowledge that you are making a prediction, as opposed to knowing the truth, by using words like “predict,” “expect,” or “estimate.” The y-intercept of an association is the same as in algebra. It is the predicted value of the dependent variable when the independent variable is zero. Be careful. In statistical scatterplots, the vertical axis is often not drawn at the origin, so the y-intercept can be someplace other than where the line of best fit crosses the vertical axis in a scatterplot.

2. Also be careful about extrapolating the data too far—making predictions that are far to the right or left of the data. The models we create can be valid within the range of the data, but the farther you go outside this range, the less reliable the predictions become. When describing a linear association, you can use the slope, whether it is positive or negative, and its interpretation in context, to describe the direction of the association.

3. Today you will think about everything you know so far about statistical analyses and will write a report with all these elements. Then you will learn a way you can report a range of values for your predictions.

4. 6-22. In 1997, an anthropologist discovered an early humanoid in Europe. As part of the analysis of the specimen, the anthropologist needed to determine the approximate height of the individual. The skeletal remains were highly limited, with only an ulna bone (forearm) being complete. The bone measured 26.4 cm in length. Your Task: Consider how you could determine how tall the humanoid was. Discuss the questions below with your team. Be ready to share your responses with the rest of the class. a)What information should you gather to answer this question? b)What process could you use to gather this information? c)What statistical information could you report back to the anthropologist? d)Once your class has decided what elements your report should contain, collect and analyze your data with your team. Write a few sentences to the anthropologist with your findings.

5. Forearm Length (cm)Height (cm) 23143 26160 27173 24175 28165 26154 29185 21147

6. 6-23. Because the height you found for the humanoid is a prediction, the actual height of the early humanoid was probably a little shorter or a little taller. In this problem, you will investigate how you can report a range of values for your prediction of the humanoid’s height. a)Look at the data you collected and your model line. Identify the point that is farthest from the line you drew. Find the residual for this point. b)In a different color, draw a dashed line that goes through this maximum residual point and is parallel to the line of your model. An example is shown below. Now draw another dashed line that is on the other side of your model and is the same distance away as the first dashed line. You have just drawn the upper and lower bounds for the variability of the data.

7. 6-23. Because the height you found for the humanoid is a prediction, the actual height of the early humanoid was probably a little shorter or a little taller. In this problem, you will investigate how you can report a range of values for your prediction of the humanoid’s height. c) Using the upper and lower bounds that you just drew, create a range of values for the possible height of a humanoid with a forearm length of 26.4 cm. d) With your team, discuss the bounds of the data. Was your model useful for predicting the height of the humanoid?