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When we standardize the values of a variable, the distribution of standardized values has a mean 0and a standard deviation 1Suppose we measure two variables Xand Yon each of several subjects. We standardize both variables and then compute the least-squares regression line. Suppose the slope of the least-squares regression line is 0.44We may conclude that

(a) the correlation will be 1/0.44

(b) the intercept will also be 0.44

(c) the intercept will be 1.0

(d) the correlation will be 1.0

(e) the correlation will also be 0.44

Short Answer

Expert verified

The correct option is (e) the correlation will also be 0.44

Step by step solution

01

Given information

(a) 1/0.44 will be the correlation.

(b) the intercept will be 0.44 as well.

(c) 1.0 will be the intercept.

(d) There will be a 1.0 correlation.

(f) the correlation will be 0.44 as well.

02

Concept

A regression line is a straight line that depicts the relationship between an explanatory variable x and a response variable y By entering any value of x into the equation of the line, you may use a regression line to anticipate the value of y for any value of x

03

Calculation

The least-square regression slope is defined as follows: b=rsXsY

Substituting the standard deviations of standardized X and Y variables, we get b=rsince sX=sY=1

In other words, the correlation is equal to the slope.

The slope of the least-squares regression line is -0.44 in this case. We can then deduce that the correlation is also -0.44

Therefore, the conclusion will be the correlation which is -0.44

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