You use a line of best fit for a set of data to make a prediction about a unknown. 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 show your work
A correlation coefficient of -0.833 indicates a strong negative linear relationship between the two variables. This means that as one variable increases, the other variable tends to decrease and vice versa.
Using a line of best fit for a set of data allows us to predict the value of one variable based on the value of the other variable. However, the predicted value may not be perfectly accurate due to variability in the data and potential outliers.
To determine if we can be confident that our predicted value will be reasonably close to the actual value, we can look at the coefficient of determination, also known as R-squared. This value ranges from 0 to 1 and represents the proportion of the variance in the dependent variable that is predictable from the independent variable.
In this case, the correlation coefficient is -0.833, which means that R-squared would be equal to 0.833^2 = 0.694. This indicates that approximately 69.4% of the variance in the dependent variable can be explained by the independent variable.
While a high R-squared value suggests a strong linear relationship and higher confidence in our predictions, it is important to consider other factors such as the spread of the data points, potential outliers, and the interpretation of the correlation coefficient in the context of the specific data set.
Therefore, with an R-squared value of 0.694, we can be reasonably confident that our predicted value will be close to the actual value, but there may still be some variability and potential for error in the prediction.