Given the following scatter diagram , the sample correlation coefficient r:
Has a positive linear correlation
Has a negative linear correlation.
Has little or no correlation.
Looks close to + 1.00
has a negative linear correlation
Positive = significant + number not above 1.00.
Negative = significant - number not above 1.00.
Little or no = ± close to zero
You can't find a positive number close to but not above +1.00?
To determine the sample correlation coefficient r from a scatter diagram, you would need to evaluate the direction and strength of the linear relationship between the two variables.
If the scatter diagram shows a clear trend where the points are increasing from left to right, it indicates a positive linear correlation. In this case, the sample correlation coefficient r would be positive.
If the scatter diagram shows a clear trend where the points are decreasing from left to right, it indicates a negative linear correlation. In this case, the sample correlation coefficient r would be negative.
If the scatter diagram shows no clear trend and the points are scattered randomly, it indicates little or no correlation. In this case, the sample correlation coefficient r would be close to 0.
If the scatter diagram shows a clear, strong, and consistent trend where the points tightly cluster around a line with a positive slope (increasing from left to right), it indicates a strong positive linear correlation. In this case, the sample correlation coefficient r would be close to +1.00.
However, without a provided scatter diagram, it is not possible to determine the exact sample correlation coefficient r. Please refer to the actual scatter diagram to evaluate the correlation.
To determine the sample correlation coefficient (r) from a scatter plot, you need to visually examine the pattern of the plotted points. The sample correlation coefficient measures the strength and direction of the linear relationship between two variables. Here's how you can interpret the options based on the scatter diagram:
1. Has a positive linear correlation: If the scatterplot shows a general upward trend from left to right, the points are clustered around a diagonal line sloping upwards. This indicates a positive linear correlation between the two variables. In this case, the correlation coefficient (r) would be positive and close to +1.00.
2. Has a negative linear correlation: If the scatterplot shows a general downward trend from left to right, the points are clustered around a diagonal line sloping downwards. This indicates a negative linear correlation between the two variables. In this case, the correlation coefficient (r) would be negative and close to -1.00.
3. Has little or no correlation: If the points in the scatterplot do not appear to follow any clear trend or pattern, and are scattered randomly, it suggests little or no correlation between the variables. In this case, the correlation coefficient (r) would be close to zero.
4. Looks close to +1.00: If the scatterplot shows a strong upward trend with the points closely clustered around a diagonal line sloping upwards, it suggests a strong positive linear correlation. In this case, the correlation coefficient (r) would indeed be close to +1.00.
To accurately determine the sample correlation coefficient (r), you would need to calculate it using a statistical software or a calculator that can perform the necessary computations based on the data points.