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Chapter 3: Q T3.8. (page 201)

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 鈭�0.44We may conclude that

(a) the correlation will be 1/鈭�0.44

(b) the intercept will also be 鈭�0.44

(c) the intercept will be 1.0

(d) the correlation will be 1.0

(e) the correlation will also be 鈭�0.44

Short Answer

Expert verified

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