V1 Module 10 Errata: Applications of Simple Linear Regression in Finance

1. The Slope Is Misstated as a Fraction of Variation

Curriculum location: Linear Regression Estimation, slope coefficient interpretation, p. 518.

"This ratio quantifies the fraction of $X$'s variation that is shared as covariation with $Y$."

The ratio $\mathrm{Cov}(X,Y)/\mathrm{Var}(X)$ is the regression slope. It has units of $Y$ per unit of $X$, can be negative, and can exceed one. Those properties are incompatible with a fraction of variation, which candidates may otherwise confuse with $R^2$.

Correct reading: The ratio $\mathrm{Cov}(X,Y)/\mathrm{Var}(X)$ estimates the change in $Y$ for a one-unit increase in $X$; it is not a share of $X$'s variation.

Candidates should track a slope's units and not interpret it as a bounded goodness-of-fit measure.

2. A Smaller p-Value Is Called a Lower Type I Error Probability

Curriculum location: Limitations of Linear Regression Models, Hypothesis Tests, the Level of Significance, and the p-Values, p. 537.

"A smaller $p$-value indicates a lower probability of making a Type I error and increases confidence in the validity of the regression model."

The $p$-value describes how extreme the observed statistic is under the null hypothesis. The preselected significance level $\alpha$, not the observed $p$-value, controls the test procedure's Type I error rate. A coefficient $p$-value also does not by itself establish that the whole regression model is valid.

Correct reading: A smaller $p$-value is stronger evidence against the tested null hypothesis. The chosen $\alpha$ controls the Type I error rate, and a $p$-value alone does not validate the regression model.

Candidates can otherwise mistake a $p$-value for either an error probability or proof that the regression model is valid.

3. The Swedish Inflation Case Calls the Non-Rejection Region Critical

Curriculum location: Limitations of Linear Regression Models, Forecasting the Swedish Inflation Rate, alternative B explanation, p. 538.

"As the $t$-statistic for the slope coefficient is $-1.0968$, it lies within the critical region."

Curriculum location: Limitations of Linear Regression Models, Forecasting the Swedish Inflation Rate, alternative C explanation, p. 538.

"As the $t$-statistic for the intercept is $0.5$, it lies within the critical region."

The case gives two-sided critical values of $\pm 2.0017$. Both test statistics fall between those bounds, so they are in the non-rejection region. A statistic in the critical region would instead lead to rejection of the null hypothesis.

Correct reading: Both $-1.0968$ and $0.5$ lie between the critical values, in the non-rejection region, which is consistent with failing to reject the respective null hypotheses.

Candidates can otherwise reverse the decision rule for a hypothesis test.

4. A Beta Confidence Interval Is Built from the Forecast Standard Error

Curriculum location: Using Linear Regression Models to Evaluate Financial Assets: The Capital Asset Pricing Model, LVMH case, Question 4 solution, Step 2, p. 560.

"Using Equation 23, ${\hat{Y}}_f\pm t_{\text{critical for }\alpha /2}{s}_{\text{Excess Return of the Market}f}$, we can compute the confidence interval as:"

${\hat{Y}}_f\pm t_{\text{critical for }\alpha /2}{s}_f={\hat{\beta }}_1\pm (\text{critical value})\times (\text{standard error})=1.3684\pm 1.96\times 0.084=1.3684\pm \mathrm{0.1646.}$

The displayed setup begins a beta confidence interval with ${\hat{Y}}_f$ and $s_f$, the estimate and standard error for forecasting a future dependent-variable value. They are not the slope estimate ${\hat{\beta }}_1$ and its standard error $s_{{\hat{\beta }}_1}$. The solution then substitutes the correct slope estimate and slope standard error, so its numerical interval is right even though the displayed setup uses the wrong statistical object.

Correct reading: A slope confidence interval is ${\hat{\beta }}_1\pm t_{\alpha /2,n-2}{s}_{{\hat{\beta }}_1}$. With the values given, $1.3684\pm 1.96\times 0.084=(1.2038,1.5330)$; the numerical answer remains correct.

Candidates should match each interval to the quantity being estimated and use that quantity's corresponding standard error.

Complete Module 10 Errata Index

Scope: Module 10, pp. 509–572 (printed page numbers).

What this review covers. Errors in the printed curriculum that would change a candidate's answer or understanding: wrong numbers, wrong formulas, reversed logic, and statements that contradict the module's own data. It does not list spelling mistakes, equation-numbering slips, or wording that is loose but defensible.

References

• Penn State STAT 501: Simple Linear Regression
• Penn State STAT 501: Simple Linear Regression Model Evaluation
• NIST/SEMATECH: Critical Values and p-Values
• American Statistical Association Statement on Statistical Significance and p-Values
• NIST/SEMATECH: Prediction

This article is an independent candidate-focused analysis of confirmed errors in the CFA Level I 2027 Curriculum, Volume 1 Quantitative Methods, Module 10 Applications of Simple Linear Regression in Finance. It is not an official curriculum errata notice.