Statistics
Statistics
4th Edition
ISBN: 9780393929720
Author: David Freedman, Robert Pisani, Roger Purves
Publisher: Norton, W. W. & Company, Inc.
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Chapter 9.1, Problem 4EA
To determine

Check whether the correlation changes or not, if double each value of x.

Expert Solution & Answer
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Answer to Problem 4EA

The correlation between y and x is the same as the correlation between x and y.

.

Explanation of Solution

From the Exercise 2, the values of x are 1, 2, 3, 4, 5

Double each value of x, and the doubled values of x are, 2, 4, 6, 8, and 10.

The average of x is obtained below:

Average=Sum of data valuesTotal number of data values=2+4+6+8+105=305=6

The standard deviation of x is obtained as follows:

SD=Sum of ((EntryAverage)2)Total number of data values  =(26)2+(46)2+(66)2+(86)2+(106)25=16+4+0+4+165=8=2.82

The average of y is obtained below:

Average=Sum of data valuesTotal number of data values=2+3+1+5+65=175=3.4

The standard deviation of y is obtained as follows:

SD=Sum of ((EntryAverage)2)Total number of data values=(23.4)2+(33.4)2+(13.4)2+(53.4)2+(63.4)25=1.96+0.16+5.76+2.56+6.765=3.44=1.85

The value of r is obtained below:

xyx in standard unitsy in standard units(x in standard units) × (y in standard units)
22262.82=1.4223.41.85=0.761.08
43462.82=0.7133.41.85=0.220.15
61662.82=013.41.85=1.300
85862.82=0.7153.41.85=0.860.61
1061062.82=1.4263.41.85=1.412.00

r=Average of (x in standard units) × (y in standard units)=(1.08)+(0.15)+(0)+(0.61)+(2.00)5=3.845=0.76

Thus, the value of r is 0.76

Thus, the correlation between y and x is the same as the correlation between x and y.

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