Unit 12 - More About Regression

Analyzing Minitab

y-int a → Coef-Constant

slope b → Coef-(Variable)

_^(sample) SD of residuals → s (avg typical error when use regression line to predict y-value)

r² → R-sq (% of variation in y-var that can be explained by the linear relationship w/ x-var)

!!! sample regression line = estimated regression line calculated from sample data

diff samples, diff regression lines/slopes → use sampling distribution of b (take many many samples) (analyze SOCS for shape (symmetric/skew, unimodal, etc.), center (mean), and spread (SD))

calculator: stat plot! scatterplot put L1 (x-values) and L2 (y-values) of data. residual plot put L1 and RESID. histogram of residuals put RESID from [2nd] [stat] [8]

know σ? → z=(b-β)/σ_b
don’t know σ? → t=(b-β)/SE_b (t-distrib with df=n-2)

Sampling distribution of b (slope)

μ_b = β

σ_b = σ/(σ_x√n) ^{_{← population SD of residuals over (population SD of x-values times square root of sample size)}}

shape approx. normal if y-values follow a Normal distribution for each x-value

What is SE_b and s

s/(s_x√(n-1))

^Sx of residual list over (Sx of x-list times square root of n-1) (get Sx from 1-VarStats. residual list is [2nd][stat][8] into L3, where L1 is x-values and L2 is y-values of OG data)

Conditions for Regression Inference

LINER

Linear relationship

• scatterplot of OG data, see approx linear pattern?

• residual plot, see random scatter/no pattern?

Independent

• experiment or 10% condition (n≤0.1N)

Normal

• histogram_{^{(/stemplot/Normal probability plot)}} of residuals, see no strong skew/outliers?

Equal SD

• residual plot, see vertical spread of residuals approx the same for above & below 0 (w/ no pattern)? (look like sandwich)

Random sampling/assignment

Parameters and their unbiased estimators

σ_b (population SD of slope) → SE_b (sample standard error of slope)

β (population slope) → b (sample slope)

α (population y-int) → a (sample y-int)