ENGR 200 – Final Exam Study Guide (Ch. 7, 8, 9, 11, 12)

🧭 Exam Overview & Strategy

Part I – True/False: conceptual questions from Ch. 7, 8, 9, 11, 12.
- Definitions: estimator vs. estimate, confidence interval vs. prediction interval.
- What p-values and significance level mean (Type I / Type II error ideas).
- Interpreting regression output: β, t, p, R², adjusted R², residual plots, VIF, Cook’s.
Part II – Calculations / Excel:
- Core single-sample ideas (mean, CI, hypothesis test) in words and simple formulas.
- Focus calculation example: Multiple Linear Regression (Chapter 12) using Excel output (same style as the Chapter 12 Excel ICE).

🔗 For extra practice on the Excel MLR part, see:
Final – MLR Excel Practice (based on Chapter 12 ICE)

✅ What You Should Be Able to Do (By Chapter)

Chapter 7 – Point Estimation & Sampling Distributions On Final

Explain the difference between a parameter (μ, σ, p) and a statistic (x̄, s, p̂).
Know that x̄ is an unbiased estimator of μ, p̂ is an unbiased estimator of p.
Describe what a sampling distribution is (distribution of x̄ from many samples).
Use the idea of Standard Error:
SE(x̄) = σ / √n (if σ known)
SE(x̄) ≈ s / √n (if σ unknown)
Explain, in words, the main idea of the Central Limit Theorem (CLT).

Chapter 8 – Confidence Intervals (Single Sample) On Final

Explain what a 95% confidence interval means in plain English.
Know when to use z vs. t for a mean:
CI for μ (σ known): x̄ ± z_α/2 · σ/√n
CI for μ (σ unknown): x̄ ± t_{α/2, n−1} · s/√n
Describe how CI width changes when:
- n increases (interval gets narrower),
- confidence level increases (90% → 99% ⇒ interval gets wider).
Excel functions to recognize:
- =AVERAGE(range), =STDEV.S(range)
- =T.INV.2T(α, df), =NORM.S.INV(prob) (conceptual recognition only).

Chapter 9 – Hypothesis Tests (Single Sample) On Final

Describe the roles of H₀ (null) and H₁ (alternative).
Explain Type I vs. Type II error in words.
Know the general test statistic shape:
t = (x̄ − μ₀) / (s/√n)
Explain how a p-value is used with α (e.g. α = 0.05) to make a decision.
Interpret “reject H₀” and “fail to reject H₀” in the context of an engineering problem.

Chapter 11 – Simple Linear Regression & Correlation On Final

Write and recognize the model:
Y = β₀ + β₁X + ε
Interpret β₀ (intercept) and β₁ (slope) in context.
Explain the difference between:
- r (sample correlation, direction & strength), and
- R² (proportion of variation in Y explained by X).
Recognize from output whether the slope is statistically significant (t, p-value).
Describe what a “good” residual plot looks like (random cloud around 0, no curve/funnel).
Excel ideas:
- Data → Data Analysis → Regression (conceptual: what it produces).
- =SLOPE(Y-range, X-range), =INTERCEPT(Y-range, X-range)

Chapter 12 – Multiple Linear Regression On Final

Write and recognize the model:
Y = β₀ + β₁X₁ + β₂X₂ + … + β_kX_k + ε
Interpret each slope as a partial effect: “Change in Y for a 1-unit change in X_j, holding other X’s constant.”
Read Excel regression output:
- Coefficients (β̂), Standard Error, t Stat, p-value, Lower/Upper 95%.
- Regression ANOVA table: SSR, SSE, MST, F, Significance F.
- R² and Adjusted R².
Explain:
- Global F-test: Does the whole model help? (At least one β ≠ 0?)
- t-test for β_j: Is predictor X_j useful, given the others?
- R² vs. Adjusted R²: why adjusted is better for comparing models.
Multicollinearity and VIF:
- Explain what multicollinearity means in plain language.
- Interpret VIF numbers (≈1–2 fine, 2–5 watch, >5 high, >10 serious concern).
Diagnostics:
- Residual plot: look for random scatter, no strong curve or funnel.
- Leverage & Cook’s distance: idea of “influential” points (few points can drive the line).
Excel:
- Data → Data Analysis → Regression (Y-range, X-range, labels, output).
- Recognize VIF from 1/(1 − R²_{Xj on others}) conceptually; in practice, use Excel / ICE.

📄 Part I – True/False Concept Checklist (by Topic)

Parameters, Estimators, Sampling (Ch. 7)

“μ, σ, p” describe the population; “x̄, s, p̂” come from the sample.
Unbiased estimator: its long-run average equals the true parameter.
As n increases, the sampling distribution of x̄ gets narrower (smaller SE).
For reasonably large n, x̄ is approximately normal even if X is not (CLT idea).

Confidence Intervals (Ch. 8)

Higher confidence ⇒ wider interval (with n fixed).
Larger n ⇒ narrower interval (with confidence level fixed).
The confidence level (e.g., 95%) is about the method, not the probability that μ is in this one specific interval.

Hypothesis Tests, p-values (Ch. 9)

p-value = probability of seeing a result this extreme or more if H₀ is true.
Type I error: rejecting a true H₀ (false alarm).
Type II error: failing to reject a false H₀ (missed detection).
Small p (e.g., < 0.05) = evidence against H₀, but not “absolute proof.”

Simple Regression & Correlation (Ch. 11)

Correlation r only measures linear association between two variables.
High correlation does not prove causation.
R² is the fraction of variation in Y explained by the regression line.
Residual plots help check linearity and constant variance assumptions.

Multiple Regression, VIF, Diagnostics (Ch. 12)

Each β̂_j is interpreted as a partial effect: one X at a time, others fixed.
Global F-test: tests “all slopes = 0” vs. “at least one slope ≠ 0.”
Adjusted R² can go up or down when you add predictors; R² never goes down.
High VIF = high multicollinearity = unstable slope estimates and large SEs.
A few high-leverage / high-Cook’s points can strongly affect the fitted model.

📊 Part II – Sample Calculation Focus: Chapter 12 Excel ICE

For the calculation part of the final, you should be comfortable using Excel regression output (like the Chapter 12 Excel ICE) to answer short questions. You are not expected to re-derive formulas from scratch.

Skills you should practice (with Excel / ICE):

Identify the regression equation from Excel output:
Ŷ = β̂₀ + β̂₁X₁ + β̂₂X₂ + … + β̂_kX_k
Decide which predictors are significant at α = 0.05 using p-values.
Interpret R² and adjusted R² and compare two models conceptually.
Use the coefficients to compute a predicted value for a given set of X’s.
Use VIF to flag multicollinearity problems and comment in plain English.
Comment on residual plots, leverage, and Cook’s distances at a basic level: “Is there any obvious problem or strong outlier driving the fit?”

🧪 For a concrete practice set (based on the GPA / study ICE idea), use:
Final – MLR Excel Practice (HTML/JS)

🧠 Final Advice

Focus first on understanding the words (what each idea means) before formulas.
Use your Term Project as a “big example” that connects confidence intervals, hypothesis tests, regression, and diagnostics.
Practice reading one or two full Excel regression outputs until it feels boring: if it’s boring, you are ready.