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If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:Group of answer choices–1.0.0.0.  1.0.either 1.0 or –1.0.Next

Question

If all the points in a scatter diagram lie on the least squares regression line, then the coefficient of correlation must be:Group of answer choices–1.0.0.0.  1.0.either 1.0 or –1.0.Next

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Solution

The answer is "either 1.0 or –1.0".

Here's why:

The coefficient of correlation, also known as the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1.

A correlation coefficient of 1 means that for every positive increase in one variable, there is a positive increase of a fixed proportion in the other. Conversely, a correlation coefficient of -1 signifies that for every positive increase in one variable, there is a negative

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Similar Questions

If the plotted points in a scatter diagram lie from upper left to lower right, then the correlation is(a) Positive(b) Zero(c) Negative(d) none of these

1. In a data set with a strong linear correlation, the points in the scatter plot approximate a line.Turn on Show least-squares fit line. The least-squares fit line is the “best-fit” line, or theline that most closely “fits” the shape of the data.A. When r = 1, how are the points in the scatter plot related to the least-squares fit line?B. Slowly decrease r. How does this affect where the points are in relation to the line?

D. Set r to –0.90. Click Same r several times. What do the least-squares fit lines forthese scatter plots have in common?A negative r indicates a negative correlation: as x increases, y tends to decrease

3. Set r to 0.00. Click Same r several times.A. Do all the least-squares fit lines for these scatter plots have the same slope?B. Do all the least-squares fit lines have the same y-intercept?C. What do all the least-squares fit lines have in common?When r = 0, there is no correlation in the data. This means that the value of y doesnot seem to be at all related to the value of x

The correlation coefficient of this scatterplot is -0.8Use the drop down menus below to describe the relationship between the two variables. The relationship between the two variables is

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