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Trial graph describe the behavior of the rel

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“Error vs. Trial” graph. Describe the behavior of the rel ationship between your errors and the order in which you saw the graphs. Did your ability seem to improve over time? Use this graph to justify your answer. (g) Suppose you guessed every value correctly; what would be the value of the correlation coefficient between your guesses and the actual correlations? (h) Suppose each of your guesses was too high by 0.2 from the actual value of the correlation coefficient. What would be the value of the correlation coefficient between your guesses and the actual correlations? (i) Does a correlation coefficient equal to 1 necessarily imply you are a good guesser? Explain.

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Chance/Rossman, 2015 ISCAM III Exploration 365 Practice Problem 5.7A Suppose that we record the midterm exam score and the final exam score for every student in a class. What would the value of the correlation coefficient be if every student in the class scored: (a) Ten points higher on the final than on the midterm? (b) Five points lower on the final than on the midterm? (c) Twice as many points on the final exam as on the midterm? Explain your answer in each part. [ Hint : You might first want to draw yourself a scatterplot of hypothetical data that fit the stated conditions.] Practice Problem 5.7B (a) The following scatterplots look at the relationships between house prices and four other variables. How does the strength of the linear relationship between price and square footage compare to the strength of the relationships in the first 3 graphs? (b) The correlations for these four graphs are 0.284, 0.394, 0.649, 0.760 Which correlation coefficient do you think corresponds to which graph? Explain your reasoning. ( Note : Each graph has the same number of houses, but you may have multiple houses indicated by an individual dot.)
Chance/Rossman, 2015 ISCAM III Investigation 5.8 366 Investigation 5.8: Height and Foot Size Criminal investigators often need to predict unobserved characteristics of individuals from observed characteristics. For example, if a footprint is left at the scene of a crime, how accurately can we estimate that person’s height based on the length of the footprint? To investigate this possible relationship, data were collected on a sample of students in an introductory statistics class. (a) Identify the observational units, explanatory variable, and response variable in this study. Observational units: Explanatory variable: Response variable: Below are the heights (in inches) of 20 students in a statistics class: 74 66 77 67 56 65 64 70 62 67 66 64 69 73 74 70 65 72 71 63 Predicting Heights (b) If you were trying to predict the height of a statistics student based on these observations, what value would you report? (c) Using the method in (b), would you always predict a statisti cs student’s height correctly? Definition: A residual is the difference between the predicted value and the observed value. If we let y i represent the i th observed value and i y ˆ represent the predicted or “fitted” value, then residual i = y i i y ˆ (d) The table below shows the residuals for each of the above heights if we use the mean height, 67.75

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