Answer:
(e) the correlation will also be -0.44
Step-by-step explanation:
If
μx = μy = 0
σx = σy = 1
m = -0.44
We know that the slope is the linear correlation is
m = r*(σy / σx)
⇒ r = (m*σx) / σy
⇒ r = (-0.44*1) / 1 = -0.44
The conclusion that gives the best answer of least squares regression line is;
Option E; the correlation will also be -0.44.
We are told that the distribution of standard values has mean of 0. Thus;
μ_x = 0
μ_y = 0
We are told that the distribution of standard values has standard deviation as 1. Thus;
σ_x = 1
σ_y = 1
We are given that the slope of the least squares regression line is -0.44. Thus;
m = -0.44
Now, formula for the slope of the linear correlation is given by;
m = r(σ_y / σ_x)
where r is the correlation. Thus;
r = m(σ_x/σ_y)
r = (-0.44)(1/1)
r = -0.44
In conclusion, looking at the given options, the only that corresponds to having the correlation as 1 is Option E.
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