# University of Massachusetts Dartmouth Economics Statistics Questions

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QUESTION 1Fill in the blanks for the following data set and calculate the correlation coefficient, r. x369y145Calculate:a) x b) y c) d) e) solve for : the correlation coefficient, = 12 points QUESTION 2Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone.x1004975992935972936y401006514566154Σx = 5814, Σx2 = 5,637,810, Σy = 570, Σy2 = 64,922 and Σxy = 546,011.Compute r. (Round to 4 decimal places.) Show Calculations:= = – = _______________________________________________________________________________________________ = * = = ____________________________ = 14 points QUESTION 3In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player’s home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.x0.2370.2610.2860.2630.2680.3390.299y1.03.95.53.83.57.35.0Σx = 1.953, Σx2 = 0.551, Σy = 30.0, Σy2 = 151.44 and Σxy = 8.735.Compute r. (Round your answer to four decimal places.) Show Calculations:= = – = ____________________________________________________________________ = * = = ____________________________ = 14 points QUESTION 4Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg).x2646294723403452y3320261329172114Σx = 297, Σy = 173, Σx2 = 11,831, Σy2 = 4101, Σ xy = 5932Compute r. (Round to 4 decimal places.) Show Calculations:= = – = _______________________________________________________________________________________ = * = = ____________________________ =