2.3-2.4 solutions

# The correlation would change if you changed the units

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36. The correlation would change if you changed the units of measurement to be grams for weight and American dollars for price (True or False) a. True b. False 37. Using information from the output above, what is the standard deviation of weight? s x = 38. Interpret the slope found in the above output in terms of X and Y. 7

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Regression (Part 2) (SOLUTIONS) Let x be the change in a stock market index in January and let y be the change in the stock market index for the entire year. Descriptive statistics from 1960 to 1997 are shown below. Descriptive Statistics: Jan, Year Total Variable Count Mean StDev Minimum Median Maximum Jan 37 0.018 0.016 0.002 0.020 0.200 Year 37 0.091 0.010 0.520 0.101 0.393 Pearson correlation of Jan and Year = 0.796 P-Value = 0.895 39. Slope is in what units in the context of this problem? Change in yearly index (dollars per share) per change in January index (dollars per share) *40. At which point on the best fitting line will you make the very best predictions? Give an (x,y) point. (Mean of X, Mean of Y) = (0.18, 0.91) Data was collected on amount of rainfall (inches) and amount of corn produced (bushels per acre) for a number of years in Kansas. The output is shown below. Predictor Coef SE Coef T P Constant 89.543 6.703 13.36 0.000 Rainfall 0.12800 0.01375 9.31 0.000 Correlation of Rainfall and Corn = 0.608 41. Find the value of r 2 for this problem. r 2 = 0.608 2 = 0.37 42. Interpret the value of r 2 in this problem. (Make sure you can interpret the values of r 2 in each of the other problems in #1-38 above.) 37% of the variation in corn production is explained by rainfall. *43. Suppose you know the value of r 2 . Can you just take its square root to get the correct correlation? Explain why or why not. If not, what other info do you need to get the sign of r? You only get the magnitude of r by taking the square root of r-squared because taking the square root of a number always gives you a positive answer. To get the sign on r, you need to look at the sign on the slope or the direction of the scatterplot. 44. An influential point always has a large residual (True or False) False; it usually does not, because it pulls the line toward itself. 45. A point with a large residual is an outlier in the vertical (Y) direction. (True or False) True 8
46. A residual is the difference between what you predicted Y to be based on the line, and what the actual of Y turned out to be in your data set. (True or False). True *47. Which of the following are affected by outliers? *48. The residual plot should show you a linear pattern if a regression line fits well. (True or False) False; the scatterplot, yes, but not the residual plot. *49. To fit a linear regression line all you need is a strong value of r. (True or False) No; you also need to look at the scatterplot because you could have a high correlation that is actually in the shape of a curve. And you could have a circular pattern with r = 0. *50. The value of r 2 is always greater than or equal to the value of r. No, it’s actually less than or equal to because you are taking the square root of a number between 0 and 1. 9
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