A. If the correlation coefficient is 0.65, what is the sign of the slope of the regression line?
B. As the correlation coefficient decreases from -0.97 to -0.99, do the points of the scatter plot move toward the regression line, or away from it?
A. Since sign of r is positive, so is the slope.
B. Toward; when it reaches -1.00, it is a straight line.
A. The sign of the slope of the regression line can be determined by the sign of the correlation coefficient. Since the correlation coefficient is positive (0.65), the sign of the slope of the regression line is also positive.
B. As the correlation coefficient decreases from -0.97 to -0.99, the points of the scatter plot move closer to the regression line. In other words, they move toward the regression line.
A. To determine the sign of the slope of the regression line, you need to consider the correlation coefficient. The correlation coefficient measures the strength and direction of the relationship between two variables.
If the correlation coefficient is positive (greater than 0), it means there is a positive linear relationship between the variables. In this case, the slope of the regression line will also be positive.
If the correlation coefficient is negative (less than 0), it means there is a negative linear relationship between the variables. In this case, the slope of the regression line will be negative.
Therefore, with a correlation coefficient of 0.65, the sign of the slope of the regression line will be positive.
B. The correlation coefficient measures the strength and direction of the linear relationship between two variables. When the correlation coefficient decreases, it means that the strength of the relationship is weakening.
For a negative correlation coefficient, as it gets closer to -1, the points of the scatter plot tend to move toward the regression line. This indicates that the points are more closely clustered around the line. In other words, the scatter plot points become more tightly aligned with the regression line as the correlation coefficient decreases from -0.97 to -0.99.
Therefore, as the correlation coefficient decreases from -0.97 to -0.99, the points of the scatter plot move closer to the regression line.