MATH 1107 · Probability and Statistics: Regression and Association

Led by Karl Pearson Simulacrum

Least squares regression, Pearson's r, R², RMSE, residuals, and the chi-square test — and why correlation still does not imply causation.

1. Module 1

   Scatterplots and the Linear Relationship

   Led by Karl Pearson Simulacrum

   The question

   Study hours vs exam marks. Fit the least squares line. What does the slope mean — and why is predicting the mark at 0 hours of study probably not meaningful?

   Outcome

   The student can fit the least squares line and interpret the slope and intercept in context.

   Sub-units

   1. ○ 1.1 Fitting a Regression Line Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   The Correlation Coefficient and Residuals

   Led by Karl Pearson Simulacrum

   The question

   r = 0.98. The residual plot shows a clear curved pattern. What does r tell you — and what does the residual plot reveal that r alone does not?

   Outcome

   The student can compute Pearson's r, construct a residual plot, and explain why correlation does not imply causation.

   Sub-units

   1. ○ 2.1 Correlation and Residuals Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   R² and RMSE: How Good Is the Model?

   Led by Karl Pearson Simulacrum

   The question

   r² = 0.96, RMSE = 2.1 marks. Does this mean 9 hours of study guarantees a high mark — and what is the difference between a high r² and a genuinely predictive model?

   Outcome

   The student can compute r², SST, SSE, SSR, and RMSE and interpret the difference between fit and predictive accuracy.

   Sub-units

   1. ○ 3.1 R² and RMSE Calculation Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   The Chi-Square Test

   Led by Karl Pearson Simulacrum

   The question

   Drink preference (tea/coffee/water) vs age group. Are they independent? Compute expected frequencies, test statistic, p-value. What does a significant chi-square tell you — and what does it not tell you?

   Outcome

   The student can conduct goodness-of-fit and independence chi-square tests.

   Sub-units

   1. ○ 4.1 Chi-Square Test Open this unit → ✓ ↻
   Open this module → Print certificate of completion
5. Module 5

   Regression, Correlation, and Causation

   Led by Karl Pearson Simulacrum

   The question

   r = 0.61 between chocolate consumption and happiness, r² = 0.37. Significant chi-square between chocolate preference and income. For each result: what does it establish, what is the most plausible alternative explanation, and what study design would establish causation?

   Outcome

   The student can distinguish association from causation and design studies that can establish causal claims.

   Sub-units

   1. ○ 5.1 Final Essay: What Statistics Can and Cannot Prove Open this unit → ✓ ↻
   Open this module → Print certificate of completion