Correlation and Regression

The method of Correlation is utilized to gauge the intensity and orientation of a bond between two different variables. Conversely, the process of Regression is utilized to estimate the value of a dependent variable, based on the worth of a minimum of one independent variable. These two techniques are of paramount importance in the field of data analysis as they assist in recognizing trends and forecasting results.

Finding the Linear Correlation Coefficient

L 6.1.3 Quiz: Two-Variable Data and Scatterplots Question 7 of 10 Which of the following graphs shows a negative linear relationship with a correlation coefficient, $r$, close to -0.5 ? c. A. Graph A B. Graph B C. Graph C D. Graph D

Determining if the Correlation is Significant

A set of data is given as follows: X = {3, 4, 5, 6, 7} and Y = {2, 5, 7, 8, 9}. Determine if the correlation between X and Y is significant.

Finding a Regression Line

Determine a power regression for the data given below. What diameter would give a length of 380.9 ? Round the numerical values of the function to three decimal places before you compute your final answer. Round your final answer to one decimal place. \begin{tabular}{|c|c||c||c||c||c||c|} \hline Diameter & 13.6 & 16.7 & 20.4 & 24.3 & 25.5 & 27 \\ \hline \hline Length & 205.7 & 239.6 & 278.1 & 317.2 & 328.9 & 343.6 \\ \hline \end{tabular}