6: Linear Correlation and Regression

Last updated
Save as PDF

Page ID: 19739

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Linear Correlation and Regression

This calculator creates a scatter plot, the regression equation, \(r\) and \(r^{2}\), and performs the hypothesis test for a nonzero correlation. Please report the error to Dr. Jessica Kuang at jkuangATvcccd.edu.

To learn how to use this calculator, please watch a short video here.

Input

Put the independent variable's data separated by commas in the first row and the dependent variable's data separated by commas in the second row, then click Plot Points and Calculate.

Explanatory/Independent Variable (x):

Response/Dependent Variable (y):

Output

Regression Equation:

\(r\):

\(r^{2}\):

Hypothesis: \(H_{0}: \rho = 0, H_{1}: \rho \neq 0\)

Hypothesis: \(H_{0}: \rho = 0, H_{1}: \rho \lt 0\)

Hypothesis: \(H_{0}: \rho = 0, H_{1}: \rho \gt 0\)

Test Statistic (\(t\)):

\(p\)-value: