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Math Help - Question about covariance

  1. #1
    Junior Member
    Joined
    Feb 2010
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    Question about covariance

    Can anyone help me with this question?

    Given:
    A data has 100 observations in a plot graph relating 2 variables, x1 and x2:
    - Mean of x1 = 10
    - Mean of x2 = 5
    - Standard deviation of x1 = 0.6
    - Standard deviation of x2 = 0.2
    - Covariance of x1 and x2 = -0.1
    (Therefore there is a relatively strong negative relationship between x1 and x2 since correlative coefficiency = -0.833333)

    Which statement summarizing relationship between x1 and x2 is true?
    a) 1 unit increase in x1 is associated with 0.1 unit decrease in x2
    b) 1 unit increase in x2 is associated with 0.1 unit decrease in x1
    c) 1 unit increase in x1 is associated with 0.17 unit decrease in x2
    d) 1 unit increase in x2 is associated with 2.50 unit decrease in x1
    e) 1 unit increase in x1 is associated with 0.28 unit increase in x2

    I know for sure it's not e), since x1 and x2 have a negative (inverse) relationship, but other than that I have no idea how to solve it. Can anyone enlighten me on this? Thanks.
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  2. #2
    Newbie
    Joined
    Apr 2011
    Posts
    21

    Re: Question about covariance

    You are dealing with the following linear regression model

    x1 = alpha + beta*x2

    So, x2 is the predictor (independent variable), whereas x1 is the response variable (dependent variable).

    You have already correctly computed the unstandardised regression coefficient, which is the correlation between the variables: -0.8333. you now want to compute the standardized coefficient, which is beta.

    Beta = covariance (x1, x2) / variance(predictor)

    Since x2 is the predictor:

    Beta = covariance(x1,x2)/variance(x2)

    Beta = -0.1/(0.2^2) = -2.5

    This means that one unit increase in the standardized x2 is associated with 2.50 units decrease in x1.





    Quote Originally Posted by Selena View Post
    Can anyone help me with this question?

    Given:
    A data has 100 observations in a plot graph relating 2 variables, x1 and x2:
    - Mean of x1 = 10
    - Mean of x2 = 5
    - Standard deviation of x1 = 0.6
    - Standard deviation of x2 = 0.2
    - Covariance of x1 and x2 = -0.1
    (Therefore there is a relatively strong negative relationship between x1 and x2 since correlative coefficiency = -0.833333)

    Which statement summarizing relationship between x1 and x2 is true?
    a) 1 unit increase in x1 is associated with 0.1 unit decrease in x2
    b) 1 unit increase in x2 is associated with 0.1 unit decrease in x1
    c) 1 unit increase in x1 is associated with 0.17 unit decrease in x2
    d) 1 unit increase in x2 is associated with 2.50 unit decrease in x1
    e) 1 unit increase in x1 is associated with 0.28 unit increase in x2

    I know for sure it's not e), since x1 and x2 have a negative (inverse) relationship, but other than that I have no idea how to solve it. Can anyone enlighten me on this? Thanks.
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