Help with covariance and the correlation coefficient

Posted on 2014-03-14 11:18:00 in Statistics by ALEX

I'm in business statistics and am really struggling with this section of the class. If anyone could help me with any part of a few problems on my homework and explain how you got it, you would be so much help!





1. A sample of 10 observations provides the following statistics:

sx = 13 , sy = 18 , and sxy = 117.22



a. Calculate sample correlation coefficient rxy.

b.Calculate the value of the test statistic.



2. In June 2009 an onslaught of miserable weather in New England played havoc with people’s plans and psyches. However, the dreary weather brought a quiet benefit to many city neighborhoods. Police reported that the weather was a key factor in reducing fatal and nondeadly shootings (The Boston Globe, July 3, 2009). For instance, it rained in Boston on 22 days in June, when 15 shootings occurred. In 2008, the city saw rain on only eight days and 38 shootings occurred. The table below shows the number of rainy days and the number of shootings that occurred in June from 2005 to 2009.



Number of Rainy Days Number of Shootings

June 2005 7 31

June 2006 15 46

June 2007 10 29

June 2008 8 38

June 2009 22 15



a. Calculate the covariance and the correlation coefficient.

b. Calculate the value of the test statistic.



3. A realtor studies the relationship between the size of a house (in square feet) and the property taxes owed by the owner. He collects the following data on six homes in an affluent suburb 60 miles outside of New York City.

a. Calculate sxy and rxy.

b. Calculate the value of the test statistic.



4. In a simple linear regression, the following sample regression equation is obtained:



y-hat = 436 ? 17x



a. Predict y if x equals ?15.



Like I said, this stuff is kind of going over my head so any help would be much appreciated!

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