University of Massachusetts Dartmouth Economics Statistics Questions

QUESTION 1

1. Fill in the blanks for the following data set and calculate the correlation coefficient, r.

   x	3	6	9
   y	1	4	5

   Calculate:a) x b) y c) d) e)
   solve for : the correlation coefficient, =
   

12 points

QUESTION 2

1. Can 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.

   x	1004	975	992	935	972	936
   y	40	100	65	145	66	154

   Σx = 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 3

1. In 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.

   x	0.237	0.261	0.286	0.263	0.268	0.339	0.299
   y	1.0	3.9	5.5	3.8	3.5	7.3	5.0

   Σx = 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 4

1. Do 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).

   x	26	46	29	47	23	40	34	52
   y	33	20	26	13	29	17	21	14

   Σx = 297, Σy = 173, Σx² = 11,831, Σy² = 4101, Σ xy = 5932Compute r. (Round to 4 decimal places.) Show Calculations:
   = = – = _______________________________________________________________________________________ = * =
   = ____________________________
   =