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Note: Your teacher will grade your responses to the follow questions to ensure you receive proper credit for your answers. You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is- 0.833. Can you be confident that your predicted value will be reasonably close to the actual value? Why or why not?

User PhilB
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Yes, with a correlation coefficient of -0.833, there is confidence that the predicted value will be reasonably close due to strong correlation.

The correlation coefficient, denoted by r, ranges from -1 to 1 and measures the strength and direction of a linear relationship between two variables.

In this case, the correlation coefficient is -0.833, indicating a strong negative linear relationship between the variables.

A correlation coefficient of -0.833 suggests a strong inverse correlation, meaning that as one variable increases, the other tends to decrease.

However, the negative sign of the correlation implies a negative slope in the regression line.

While a correlation coefficient of -0.833 indicates a strong relationship, it does not necessarily guarantee the accuracy of individual predictions.

The correlation coefficient specifically measures the strength and direction of a linear relationship, but it does not provide information about the spread or variability of the data points around the line of best fit.

To assess the reliability of predictions, it is essential to consider the scatter or dispersion of data points.

A high correlation coefficient alone does not ensure that the predicted value will be close to the actual value, as there may be considerable variability around the regression line.

It is crucial to examine the residual plot or other measures of prediction accuracy to better evaluate the reliability of predictions.

Therefore, while the strong negative correlation suggests a relationship, confidence in the accuracy of individual predictions also depends on the spread of data points around the line of best fit.

User Kevin Danikowski
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