Correlation & Linear Regression Using a TI-Nspire

Bivariate Data The use of scatter plots can provide an initial visual aid in describing any relationship that might exist between two variables.

Plotting the Data 1.Enter bivariate data into a new “List & Spreadsheet.” 2.Insert a new tab “Data & Statistics” and set the x and y axes to the proper variable. 4.The scatterplot shows there is a positive correlation between the time spent studying and the score on the test.

Strength of Relationship The more ‘linear’ the data, the stronger the correlation. The measure of the strength of the linear relationship is determined by calculating Pearson’s correlation coefficient which is denoted by, r. The value of r does not depend on the units or which variable is chosen as x or y. The value of r lies in the range -1  r  1. – A positive r indicates a positive relationship – A negative r indicates a negative relationship. The closer to 1 or -1, the stronger the correlation.

Strength of Relationship This table provides a good indication of the qualitative description of the strength of the linear relationship and the qualitative value of r. 1.0 Perfect positive linear association (1.0) 0.8 Strong positive linear association 0.6 Moderate positive linear association 0.4 Weak positive linear association No linear association Weak negative linear association -0.6 Moderate negative linear association -0.8 Strong negative linear association Perfect negative linear association (-1.0)

Calculating r 1.Enter (or go back to) the bivariate data into a new “List & Spreadsheet.” 2.Run Two-Variable Statistics Calculation 3.Select appropriate x and y variables. 4.Scroll down to find r

Linear Regression

Finding the Regression Line The scatterplot below shows a student’s Regents Test Score v. Hours of Study Since r = 0.85, a strong linear relationship exists and the equation for the line of best fit can be written and used.

Finding the Equation for the Line of Best Fit

Plotting the Regression Line Method 2 On the existing scatterplot, go to: Menu  Analyze  Regression  Show Linear

Goodness of Fit A residual value is the vertical distance an observed value (data) is from the predicted value (line). In general, a model fits the data well if the differences between the observed values and the model's predicted values are small and unbiased.

Using the Regression Line 1.If there is no linear correlation, don’t use the regression equation to make predictions. 2.When using the regression equation for predictions, stay within the scope of the available data. 3.Do not conclude that correlation implies causation. There could be other lurking variables.

Spurious Correlations