University of Massachusetts Dartmouth Economics Statistics Questions

Description

QUESTION 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

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

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

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:
= = – = _______________________________________________________________________________________ = * =
= ____________________________
=

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