Calculator Data Entry and Correlation Errors
Accurate linear regression on a graphing calculator requires entering x-values in L1 and y-values in L2 in the correct order — a practical statistics skill in enVision Algebra 1 Chapter 3 for Grade 11. Swapping lists produces an inverted regression equation with incorrect slope and intercept. The correlation coefficient r ranges from -1 to 1: r = -1 is perfect negative correlation, r = 0 is no linear correlation, and r = 1 is perfect positive correlation. A common error is misreading r = -0.85 as weak correlation — the magnitude 0.85 indicates strong correlation; the negative sign indicates direction only.
Key Concepts
Proper calculator setup requires $x$ values in L1 and $y$ values in L2. Correlation coefficient $r$ ranges from $ 1$ to $1$, where $r = 1$ indicates perfect negative correlation, $r = 0$ indicates no linear correlation, and $r = 1$ indicates perfect positive correlation.
Common Questions
Why must x-values be in L1 and y-values in L2 for linear regression?
The calculator performs LinReg(ax+b) using L1 as the independent variable and L2 as the dependent variable. Swapping them reverses the regression, producing a different (incorrect) equation for your intended model.
What does r = -0.85 mean about the linear relationship?
The correlation is strong (|r| = 0.85 is close to 1) and negative (as x increases, y decreases). Strength is determined by |r|, not the sign.
What is the difference between r = 0.2 and r = 0.9?
r = 0.2 indicates a weak positive linear relationship; the points are widely scattered. r = 0.9 indicates a strong positive linear relationship; the points cluster closely along a line.
What does r = 0 mean in a scatter plot?
r = 0 means there is no linear correlation. The data may still show a nonlinear relationship (like a parabola), but a straight line does not fit the data.
How does entering height in L2 and weight in L1 by mistake affect the regression?
The calculator will regress weight as the function of height instead of height as a function of weight, producing an equation with inverted roles and an incorrect slope and intercept for the intended model.