A procedure used for finding the equation of a straight line which provides the

Question

A procedure used for finding the equation of a straight line which provides the best approximation for the relationship between independent and dependent variables is

Select one:

A. correlation analysis

B. mean squares method

C. least squares method

D. most squares method

E. None of the above answers is correct

In regression and correlation analysis if r2=1, then sum squares due to error

Select one:

A. must also be equal to one

B. must be equal to zero

C. can be any positive value

D. must be negative

E. None of the above answers is correct

If the coefficient of determination is a positive value, then the regression equation

Select one:

A. must have a positive slope

B. must have a negative slope

C. could have either a positive or negative slope

D. must have a positive intercept

E. None of the above answers is correct

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If there is a very strong correlation between two variables, then the coefficient of correlation must be

Select one:

A. much larger than 1, if the correlation is positive

B. much smaller than 1, if the correlation is negative

C. both a and b are correct answers

D. None of the above answers is correct

Question 10

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If coefficient of correlation is a positive value, then the slope of the regression line

Select one:

A. must be positive

B. can be either negative or positive

C. can be zero

D. None of the above answers is correct

Question 11

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If the coefficient of correlation is a negative value, then the coefficient of determination

Select one:

A. must also be negative

B. must be zero

C. can be either negative or positive

D. must be positive

E. None of the above answers is correct

Explanation / Answer

A procedure used for finding the equation of a straight line which provides the best approximation for the relationship between independent and dependent variables is
Select one:

C. least squares method [ANSWER, by definition]

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In regression and correlation analysis if r2=1, then sum squares due to error

B. must be equal to zero [ANSWER]

This means all the points perfectly lie on the line, so the sum of squared errors must be 0.

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If the coefficient of determination is a positive value, then the regression equation
Select one:

C. could have either a positive or negative slope [ANSWER]

The coefficient of determination is always nonnegative, so it doesn't tell us anything about the sign of the slope.

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9.

If there is a very strong correlation between two variables, then the coefficient of correlation must be

Select one:

D. None of the above answers is correct [ANSWER]

It must either be close to -1 or 1. The second best answer is OPTION B, but I don't call -1 "much smaller than 1", so I chose D.

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