2. Ages of Famous Personalities
View each slide, one at a time.
Guess and record the age of each celebrity (y-coordinate)
Then view the last slide to see the actual ages (x-coordinate)
Graph all ordered pairs on a coordinate plane labeled “Actual Ages” on the x-axis and “The Ages I Guessed” on the y-axis.
Draw a trend line. A line that fits all of the data.
Find the equation of the trend line.
Use the equation to predict the age you would guess for an 80 year old. (plug in 80 for the “actual age” variable.)
Use the equation to predict the actual age of a person when “your guessed age” is 10.
Show your work!
Sometimes we have to extend data to cover places in which no data were measured. For example, we try to predict what the demand for electric power will be in ten years in order to plan for new power plants, and all we have available is information about how demand has grown in the past ten years. We have to extrapolate our information into the future.
Extrapolation is prediction outside the range of our data; interpolation is prediction within the range. Both can be done badly for two common reasons. First, the model is wrong. Models are important to interpreting what we observe, both in science and in ordinary life. Data rarely speaks by itself, leaving it to a model to unify and explain the data.
Second, even if the model is not wrong there are probably hidden complications. It is possible to find a model that can explain the workings of some theory within the range of observations, but which has unknown, perhaps poor, reliability outside the range.
Both wrong models and hidden complications occur in calculating chemical and radiation risks. The commonly accepted model is that risk is proportional to dosage. If we look at radiation risk alone, we find evidence that risk is proportional to dosage. Figure 1, for example, shows risk versus dosage of ionizing radiation. The data come from accidents involving large doses of radiation. This presents a problem in that the range of observed dosage versus risk is unusual. We are interested mainly in the relationship down in the region of the little box in the corner of the graph. There is no way of knowing what the true relationship of dosage to risk is actually, but one model is that of a linear increase of risks with dosage beginning with the origin of the graph. It seems reasonable that zero dosage means zero risk, and, therefore, the curve must pass through the origin. However, this doesn't limit the range of possible relationships at all. People have proposed all sorts of alternative relationships in this region, as shown with dashed lines of Figure 2.

3. Melissa McCarthy

4. Will Smith

5. Johnny Depp

6. Angelina Jolie

7. Dewayne Michael Carter Jr.

8. Chris Hemsworth

9. Beyonce

10. Denzel Washington

11. Leonardo DiCaprio

12. Oprah Winfrey

13. Ellen DeGeneres

14. Emma Watson

15. Cuba Gooding Jr.

16. Tom Cruise

18. Owen Wilson

19. Taylor Swift

20. Chris Pratt

21. Pauley Perrette

22. Russell Crowe

23. Jaden Smith

24. Jennifer Lopez

25. Ashton Kutsher

26. Jennifer Aniston

27. Robert Pattinson

28. Selena Gomez

29. Celebrity Ages Melissa McCarthy 46 Tom Cruise 54 Stefani Germanotta 31
(Lady Gaga)
Will Smith 48
Johnny Depp 53
Owen Wilson 48
Angelina Jolie 41
Taylor Swift 27
Dewayne Michael Carter Jr (Lil Wayne)
Chris Pratt 37
Pauley Perrette 48
Chris Hemsworth 33
Russell Crowe 53
Beyonce 38
Jaden Smith 18
Denzel Washington 62
Jennifer Lopez 47
Leonardo DiCaprio 42
Ashton Kutsher 39
Oprah Winfrey 63
Jennifer Aniston 48
Ellen DeGeneres 59
Robert Pattinson 30
Emma Watson 27
Selena Gomez 24
Cuba Gooding Jr. 49