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Learn how to analyze bivariate data using scatter plots, calculate Pearson's correlation coefficient, find regression lines, and interpret relationship strength. Explore the nuances of correlation and regression for data analysis. Avoid pitfalls and misconceptions in statistical analysis.
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Correlation& LinearRegression Using a TI-Nspire
Bivariate Data • The use of scatter plots can provide an initial visual aid in describing anyrelationship that might exist between two variables.
Plotting the Data • Enter bivariate data into a new “List & Spreadsheet.” • Insert a new tab “Data & Statistics” and set the x and y axes to the proper variable. • 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 rdoes not depend on the units or which variable ischosen as x or y. • The value of r lies in the range -1 r 1. • A positive rindicates a positive relationship • A negativerindicates a negativerelationship. • 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.
Calculating r • Enter (or go back to) the bivariate data into a new “List & Spreadsheet.” • Run Two-Variable Statistics Calculation • Select appropriate x and y variables. • Scroll down to find r
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.
Plotting the Regression Line Method 2 On the existing scatterplot, go to: • Menu Analyze Regression Show Linear
Goodnessof Fit • A residual valueis 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 • If there is no linear correlation, don’t use the regression equation to make predictions. • When using the regression equation for predictions, stay within the scope of the available data. • Do not conclude that correlation implies causation. There could be other lurking variables.
