HW_Temp Proxies go to the Movies

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Temple University *

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0836

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Electrical Engineering

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Dec 6, 2023

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EES 0836 Temperature Proxies go to the Movies Disasters: Geology vs. Hollywood Introduction "Everyone talks about the weather, but no one ever does anything about it." --Mark Twain Mark Twain's famous quip no longer rings true. Apparently, humans are doing a great deal to influence the weather. At least that is what the "hockey stick" plot shows, published by Mann et al. in 1999 in an issue of Nature (inset image). The plot shows time on the x-axis and global average temperature relative to 1995 in degrees Celsius on the y-axis. Notice the rise of approximately half of a degree coinciding with the industrial revolution. Why is the plot disputed? Doesn't it clearly show that the temperature was stable for hundreds of years, and then suddenly shot up? Well, the catch is that we cannot go back in time and record the actual temperatures hundreds of years ago, so the plot is based on "proxy" data. A temperature proxy is something we can measure that is not temperature, but is related to temperature "well enough" to be used as a substitute. Mann et al. used combinations of paleoclimate data – tree rings, coral growth, stable isotope data, etc. – to deduce historic temperatures. For example, the amount a tree grows each year can be seen in the rings, and trees tend to grow more in warmer years. The interpretation of the proxy data is at the heart of the dispute over this famous plot. Learning Objectives ● Understand how proxies can be used to help make predictions. (1, 2, a, b) ● Explain the limitations with proxies relative to their use in climate science. (1, 2, c) Part 1 : A Hollywood Analogy Let's get the flavor of proxies by investigating a different type of data set. Suppose we want to predict the first-year box office receipts of a new movie that is based on a best-selling book. Hollywood has made movies based on books many times before, so we have earnings data for previous movies that are spun off books. We can compare with three things that might be related (proxies). Three possible proxies: 1. the movie's production costs (big budget films tend to make more money) 2. the amount of money spent on promotion (more ads, more sales) 3. total book sales (movies are usually based on best-sellers)

EES 0836 Here is our data set (all numbers are in millions of dollars): Box Office Receipts Production Costs Promotion Costs Book Sales 85.1 8.5 5.1 4.7 106.3 12.9 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 89.3 10.2 4.5 7.9 Using the provided graph, plot the Production Costs (horizontal X values) vs. the Box Office Receipts (vertical Y values). If you plot the data correctly, your plotted points should be close to the best fit line (thin red line).

EES 0836 Questions 1. Do you think it is reasonable to use production costs to predict box office receipts even though the line does not fit the data perfectly? Why or why not? I still do think it is reasonable to use production costs to predict box office receipts. The line of best fit is not an exact prediction of the values, just the overall average. 2. If you were a Hollywood producer, would you rather your new movie plotted above or below the line? Why? I would rather my new movie plotted above the line of best fit, which shows better box office success. 3. Plotted below are the two other proxies for box office receipts. Of all three proxies plotted, which do you think is the best predictor? Explain your reasoning. Clearly, all three proxies hold some predictive value (there is at least some correlation between all three and the box office receipts). Is it possible to combine the information from all three to come up with an even better predictor? The easy answer is: Yes . This can be accomplished using a method called "multiple linear regression," which tells us what weighted combination of our three predictors yields the best proxy. For this data set, it turns out the best predictor is the combination shown in the last column of the table below. (As before, all numbers are in millions of dollars.) Finish filling in the values for the combined proxy in the last column of the table. NOTE there is an order of operations issue here. You need to do the multiplication of the values in the

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