Question

In a simple linear regression analysis, the correlation coefficient ( ) and the slope (m) _____ have the same sign. a. always b. sometimes c. never

Answer 1

Answer:

a. always

Step-by-step explanation:

In a simple linear regression, the slope measures the steepness of the linear relationship between the two variables, it ranges from (-∞ to +∞ ) while the correlation coefficient measures the tightness of the linear relationship between the two variables, it ranges from (-1 to +1 ).

So the correlation coefficient and the slope will always have the same sign though their values might differ.

Answer 2

In a simple linear regression analysis, the correlation coefficient ( ) and the slope (m) always  have the same sign .

In a simple linear regression,

Both quantify the direction and strength of the relationship between two numeric variables.

When the correlation (r) is negative, the regression slope (b) will be negative.

When the correlation is positive, the regression slope will be positive.

The slope measures the steepness of the linear relationship between the two variables,

It ranges from (-∞ to +∞ ) while the correlation coefficient measures ,

The tightness of the linear relationship between the two variables, it ranges from (-1 to +1 ).

So, The correlation coefficient and the slope will always have the same sign though their values might differ.

Hence, In a simple linear regression analysis, the correlation coefficient ( ) and the slope (m) always have the same sign .

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