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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. Enter bivariate data into a new “List & Spreadsheet.”
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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.
