Intro to multiple lineair regression

21 important questions on Intro to multiple lineair regression

Q: What is the general multiple linear regression model?

Formula:

Q: What is the goal of multiple regression?

To understand how Y depends jointly on X₁…Xₖ, and how strong those relationships are.

Q: What are the model assumptions in MLR?

Assumptions:
  • Higher grades + faster learning
  • Never study anything twice
  • 100% sure, 100% understanding
Discover Study Smart

Q: What is “no perfect multicollinearity”?

No independent variable can be a strict function of another (e.g., X₂ = X₁² is not allowed in Ch. 20).

Q: What is the meaning of β₁ in MLR?

The expected change in Y when X₁ increases by 1 holding all other X’s constant (ceteris paribus).

Q: Interpretation of β₀ in MLR?

The expected Y when all X’s = 0, but only meaningful if X=0 is realistic for all predictors.

Q: What is the prediction equation?

FORMULA:

Q: What are residuals?

ANSWER:

Q: WHAT IS SSE?

ANSWER:

Q: Why does MLR use df = n – (k+1)?

Because we estimate k+1 parameters (β₀…βₖ).

Q: What are the three sums of squares in regression?

  • SSR = regression explained variation
  • SSE = residual unexplained variation
  • SST = total variation (SST = SSR + SSE)
  • Q: What are the degrees of freedom in ANOVA?

  • Regression: k
  • Residuals: n − (k + 1)
  • Total: n − 1
  • Q: What is the F-statistic in MLR?

    Answer:

    Q: What does the F-test check in MLR?

    Wether the model is useful:
    H₀: β₁ = β₂ = … = βₖ = 0
    H₁: at least one βᵢ ≠ 0

    Q: What is the rejection region for the F-test?

    Answer:

    Q: What is R²?

    Answer:

    Q: What is adjusted R²?

    Formula:

    Q: What is the t-statistic for testing βᵢ?

    Answer:

    Q: What is the most important test in MLR?

    Testing whether a single independent variable is individually significant:
    H₀: βᵢ = 0
    H₁: βᵢ ≠ 0

    Q: Degrees of freedom for t-tests in MLR?

    df = n – (k + 1)

    Q: When is Xᵢ significant?

    If 0 is not inside the CI, or
    |t| ≥ tα/2.

    The question on the page originate from the summary of the following study material:

    • A unique study and practice tool
    • Never study anything twice again
    • Get the grades you hope for
    • 100% sure, 100% understanding
    Remember faster, study better. Scientifically proven.
    Trustpilot Logo