Thread: 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.

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.

Originally Posted by Selena

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.