Interpret Scatter Plots - INTERPRETING SCATTER PLOTS AND...

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Unformatted text preview: INTERPRETING SCATTER PLOTS AND TWO-VARIABLE STATISTICS Activity 1: Match the scatter plot to the correct correlation coefficient: 1. 0.14 2. ‐0.99 3. 0.43 4. ‐0.77 Activity 2: A zoologist was interested in predicting the weight of alligators by simply measuring their length. Some brave researchers went out to an alligator preserve in the Everglades, and measured 21 alligators’ lengths and weights. Best ft linear equation: y = 5.9x ‐ 393, r = 0.93 a) What is the slope of the linear model? Interpret this value in context of the data. b) What is the y‐intercept of the linear model? Interpret this value in context of the data. Does this interpretation make sense in context? Why (not)? c) One alligator the researchers named “Fluffy” was too aggressive to be weighed. They did get Fluffy’s length, though: 108 inches. Predict her weight using the model. d) Even though the correlation between weight and length is high (0.93), There may be a better equation to model this relationship. Why? Activity 3: Mr. Theil collected arm span and height data for a larger group of students. He also wanted to see if the relationship between height and arm span was different for males and females. Correlation coefficients: for females, r= 0.917 and for males, r = 0.616 a) For which group, males, or females, is the relationship between height and arm span stronger? b) Give one piece of visual evidence for your conclusion in part a). c) Give one piece of numerical evidence for your conclusion in part a). d) Tracy’s arm span is 170 cm long. Predict her height, using the appropriate best ‐ft linear model. e) Chuckie’s Arm span is 180 cm. Predict his height. f) Which prediction, Tracy’s or Chucky’s, is probably more accurate? Provide evidence and/or specifc reasoning for your decision. g) One person, “Kelly,” has an arm span of 168 cm, and a height of 170 cm, and was left off the plot. You don’t know if Kelly is male or female. What’s your best guess? Provide evidence for your conclusion. h) How confdent are you with your decision in g)? Absolutely sure, pretty sure, or not very sure at all? Explain. i) There’s a point plotted at (212, 181). Write a sentence that describes the gender and appearance of this person. How are they considerably different from the rest of the people in this study? Be specifc. j) There’s a point plotted at (175, 188). Write a sentence that describes the gender and appearance of this person. How are they considerably different from the rest of the people in this study? Be specifc. PROBLEM 1: Do higher grossing movies in the US tend to be higher-grossing internationally as well? The following table contains the box office receipts for the ten highest grossing movies in history (as of 2007). The numbers are in millions of dollars and adjusted for inflation. Movie Domestic International Receipts Receipts Titanic 601 1235 Star Wars 461 337 Shrek 2 437 444 ET 435 322 Star Wars: Phantom Menace 431 491 Pirates of the Caribbean: Dead Man’s 417 592 Chest Spider-Man 404 418 Star Wars: Revenge of the Clones 380 468 The Lord of the Rings: The Return of the 377 752 King Spider-Man 2 373 410 a. Plot the relationship on a scatter plot. b. Find the equation of the line of best ft. Use this model to predict the international box office gross for a movie which brings in $500 million dollars in the US. c. Interpret the value of the slope in context of this situation. d. Interpret the y‐intercept of the model in context. Do you feel this interpretation has any real‐world value? Explain. e. Suppose that Titanic were removed from this data set. How would this removal change the value of the slope and the intercept of the linear model? f. Suppose that Titanic were removed from this data set. How would this removal change the value of the correlation coefficient? Explain why. g. Create a new scatter plot, determine the new equation of the line of best ft, and determine the new correlation coefficient after removing Titanic from the data set. h. Even if you removed Titanic from the data set, and computed a new linear model and correlation coefficient, why might it be inappropriate to use them to make predictions about the international box office income of other movies that premiere in the US? PROBLEM 2: The data provided in the table below are the gold medal winning long jump distances for the men’s and women’s divisions at the Olympics from 1948 to present. Year Men’s Distance (m) Women’s Distance (m) 1948 7.82 5.69 1952 7.57 6.24 1956 7.83 6.35 1960 8.12 6.37 1964 8.07 6.76 1968 8.90 6.82 1972 8.24 6.87 1976 8.34 6.72 1980 8.54 7.06 1984 8.54 6.96 1988 8.72 7.40 1992 8.67 7.14 1996 8.50 7.12 2000 8.55 6.99 2004 8.59 7.07 Make three scatter plot graphs – Men’s Distance vs. year, Women’s Distance vs. year, and Women’s Distance vs. Men’s Distance (or vice versa). (You could also try to make a double scatter plot with year on the x-axis and both men’s and women’s distances on the y-axis) a. Determine the equations of the lines of best ft and the correlation coefficients for each scatter plot. b. What do each of these equations and coefficients tell you about distances over time, and men’s distances compared to women’s distances. c. According to the scatter plots and trends, will women ever “catch up” to men in terms of distance jumped. ...
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