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.

Melissa McCarthy

Will Smith

Johnny Depp

Angelina Jolie

Dewayne Michael Carter Jr.

Chris Hemsworth

Beyonce

Denzel Washington

Leonardo DiCaprio

Oprah Winfrey

Ellen DeGeneres

Emma Watson

Cuba Gooding Jr.

Tom Cruise

Owen Wilson

Taylor Swift

Chris Pratt

Pauley Perrette

Russell Crowe

Jaden Smith

Jennifer Lopez

Ashton Kutsher

Jennifer Aniston

Robert Pattinson

Selena Gomez

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. 34 (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