Summary: Statistics
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1 8 Simple Lineair Regression (2)
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What does S(res) represent?
The standard deviation of residuals – how far an observation typically lies from the regression line. -
What does SE(b₁) represent?
The standard error of the slope. It measures how much the slope b₁ would vary if we repeated sampling many times. -
What is SSR (Regression Sum of Squares)?
The explained variation — how much ŷ values differ from the mean of y. -
What is SSE (Error Sum of Squares)?
The unexplained variation — how much actual y’s differ from their predicted ŷ. -
What is SST (Total Sum of Squares)?
Total variation of y around its mean. -
How is R² (Coefficient of Determination) defined?
Formula: -
t-Test for the Slope (b₁) - What are the hypotheses?
- H0:β1=0H_0: \beta_1 = 0 (no relationship)
- H1:β1≠0H_1: \beta_1 \neq 0 (there is a relationship)
- H0:β1=0H_0: \beta_1 = 0 (no relationship)
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t-Test for the Slope (b₁) - What is the test statistic?
Formula: -
t-Test for the Slope - What are the degrees of freedom?
df = n − 2 -
t-Test for the Slope (b₁) - Decision rule (α = 0.05, two-tailed)?
Reject H₀ if |t| > t₍ₐ/₂, n–2₎.
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Topics related to Summary: Statistics
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Simple Lineair Regression
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Probability Distributions & Descriptive Statistics - Probability Theory
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Probability Distributions & Descriptive Statistics - Discrete & Continuous random variables
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Probability Distributions & Descriptive Statistics - Bernouilli and Binomial Distribution
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Probability Distributions & Descriptive Statistics
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Probability Distributions & Descriptive Statistics - Joint Probability Distributions
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Sampling Theory & Sample Mean
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Interval Estimation & Hypothesis testing
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Proportion variation, confidence intervals for mu, p and sigma^2
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Intro to multiple lineair regression
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Extending the multiple lineair regression model
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Multiple linear regression model violations
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Introduction to Confidence Intervals and test for two parameters
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CI's and tests for ratio of two population variances, difference between two population proportions
