Math 1153 - 13 October 2026 - Chapter 6

Overview

Mike Jacobsen reviews Chapter 6 association and correlation, using a 12-year dataset of online-fraud losses from 2001–2012 to practice calculator scatter plots and describe direction, form, strength, and outliers. He explains the Pearson correlation coefficient’s range and limitations, connects its calculation to paired z-scores, and demonstrates the TI-84 setup for reporting r before previewing linear regression in Chapter 7.

Key takeaways

Before interpreting Pearson’s r, inspect the scatter plot: r measures linear association, so a curved relationship can make its value misleading.
Pearson’s r ranges from −1 to +1, and its sign matches the direction of a linear relationship: positive for an upward trend and negative for a downward trend.
A standardized paired observation contributes the product zₓzᵧ to the correlation formula; points on opposite sides of the two means contribute negative products.
In the 2001–2012 online-fraud example, losses generally rise and level off, while the unusually low 2010 value stands out as a possible outlier.
On a TI-84, enable DiagnosticOn through the catalog, then use STAT → CALC → LinReg(a+bx) with L1 and L2 to display the correlation coefficient.
A rule-of-thumb judgment about correlation strength must account for context: a small association could be useful in one application and inadequate for high-stakes engineering.

Chapters

0:00 Exam 2 Schedule, Calculator, and Study Plan

Exam 2 can be scheduled Monday, October 19 through Thursday, October 22; students should check the updated Canvas and ICU Gmail instructions.
A calculator is required, and Mike Jacobsen recommends bringing one rather than relying on a possible testing-center spare.
The permitted notes sheet may be printed or handwritten on both sides; handwritten notes must be in pen.
Jacobsen recommends catching up on quizzes and MyLab homework before practicing with the sample exams.

4:26 Online-Fraud Dataset: Explanatory and Response Variables

The example pairs years 2001–2012 with annual online-fraud losses measured in billions of dollars.
Year is the explanatory variable and belongs in calculator list L1 and on the horizontal axis; fraud loss is the response variable and belongs in L2 and on the vertical axis.
Each year must stay paired with its corresponding loss—for example, 2007 matches $3.7 billion, not the next year’s value.

6:09 TI-84 Scatter-Plot Setup and Data Entry

Turn on Stat Plot once by pressing 2nd and Y=, selecting Plot1, and ensuring the plot is on and set to the scatter-plot icon.
Enter the 12 years in L1 and the matching fraud-loss figures in L2 using STAT and Edit.
Jacobsen repeats the setup after a screen-sharing problem and clarifies that STAT alone opens the list editor.

13:38 Use ZoomStat to Display the Scatter Plot

After entering both lists, press ZOOM and choose option 9, ZoomStat, to fit the calculator’s viewing window to the data.
The resulting scatter plot is a time-series plot because the horizontal variable is year, while remaining a scatter plot of paired numerical values.
The calculator workflow is summarized as entering the data, selecting ZoomStat, and viewing the plotted result.

16:29 Describe the Fraud-Loss Trend: Direction, Form, and Strength

From 2001 to 2012, online-fraud losses generally rise, so the overall direction is positive.
The pattern grows steadily at first and then levels off in later years, supporting a nonlinear description rather than a simple straight-line trend.
The relationship appears stronger early in the series and more variable later, so its visual strength weakens over time.
The 2010 loss is unusually low compared with neighboring years and is identified as a possible outlier.

27:46 Pearson’s r Measures Linear Association

The Pearson sample correlation coefficient, denoted r, summarizes the direction and strength of a linear relationship between two numerical variables.
Its values range from −1 to +1: values near +1 indicate strong positive linear association, while values near −1 indicate strong negative linear association.
Jacobsen stresses that r does not measure nonlinear association; calculating it for curved data can produce an uninformative result.

31:49 Classify Scatter Plots Before Interpreting r

The worked graph examples distinguish no apparent relationship, linear relationships, and a clearly curved nonlinear relationship by asking whether a straight line fits the points reasonably well.
For linear plots, rising points indicate a positive relationship and falling points indicate a negative relationship; r has the same sign as that direction.
For the nonlinear curve, the points still have an overall direction, but students should not assign r a positive or negative interpretation because the linear statistic is inappropriate.

42:00 The Correlation Formula Standardizes Both Variables

Jacobsen presents r as the sum of paired products of standardized x- and y-values divided by n − 1.
Each z-score subtracts its variable’s mean and divides by its standard deviation: x uses x̄ and sₓ, while y uses ȳ and sᵧ.
The formula provides a conceptual explanation of correlation even though the calculator will do the arithmetic.

45:38 Use x̄ and ȳ to Determine Z-Score Signs

A point above ȳ has a positive y z-score; a point below ȳ has a negative y z-score.
A point to the right of x̄ has a positive x z-score; a point to the left has a negative x z-score.
Drawing the x̄ and ȳ reference lines divides a scatter plot into regions that reveal the signs of each point’s paired z-scores.

47:38 How Paired Z-Score Products Reveal Correlation Direction

For points where x and y lie on opposite sides of their respective means, one z-score is positive and the other negative, making their product negative.
In Jacobsen’s descending example, most paired products are negative, so their sum—and therefore r—is below zero.
The products’ magnitudes as well as their signs contribute to r; the calculator avoids the extensive hand calculation across all observations.

51:45 Interpret Correlation Strength in Context

Values of r near zero suggest little linear association, while values farther from zero indicate stronger linear association under the course’s rough rule of thumb.
A near-zero r does not rule out a nonlinear pattern, which is why the scatter plot must be checked before interpreting the statistic.
Jacobsen contrasts contexts: a small correlation might still matter in stock-market analysis, while rocket structural engineering could demand a relationship near 0.999.

59:31 Enable TI-84 Diagnostics and Run LinReg(a+bx)

Enable the correlation diagnostic by pressing 2nd and 0 to open the catalog, scrolling to DiagnosticOn, and pressing ENTER until the calculator displays “Done.”
Use STAT, move to CALC, and select option 8, LinReg(a+bx); verify Xlist is L1, Ylist is L2, and the frequency list is blank.
The demonstration calculates r for the earlier curved fraud-loss data only to show the procedure; Jacobsen reiterates that this nonlinear dataset should not be interpreted using r.

1:08:19 Chapter 7 Preview: Linear Regression

Jacobsen says the z-score formula is a conceptual explanation rather than a formula students need to memorize for calculator calculations.
LinReg(a+bx) will become useful in Chapter 7, where the meanings of the regression coefficients a and b will be developed.
The next class will revisit the TI-84 steps and calculate correlation for a more appropriate linear example.

Summary, takeaways, and chapters were generated by AI from the video's transcript and may contain errors. The video belongs to its creator, Mike Jacobsen.