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Statistical Analysis Insights Examined Through Hypothesis Testing, Residual Analysis, and Model Evaluation Techniques

Explore the impact of influential factors, spread of x values, and model validity through hypothesis testing, residual analysis, and prediction intervals with detailed Minitab outputs. Examine the significance of coefficients, confidence intervals, and prediction intervals in interpreting statistical results.

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Statistical Analysis Insights Examined Through Hypothesis Testing, Residual Analysis, and Model Evaluation Techniques

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  1. Stat 322 – Day 29

  2. HW 8 • See updated version online • Delete question 6 • Please always define parameters, state hypotheses and comment on technical conditions, include Minitab output • Hints on question 2?

  3. Exam 2 • Problem 1: Potentially influential vs. influential • Problem 2: Effect of spread of x values vs. information about form • Problem 3: • “validity” = residual analysis, “useful” = model utility test, “appear to be” = find p-value • Coefficient of machine type with age held fixed, so compared to machines of similar ages • Confidence interval vs. prediction interval

  4. Exam 2 – Problem 4 • H0: b1=20 vs. Ha: b1≠20 • t = (22.257 – 20)/5.002 • Degrees of freedom = n-2 = 5 • Two-sided p-value • Do not have evidence to doubt 20 cm3/mm

  5. Exam 2 – Problem 4 • s, measures the variability in the response variable at each x (standard dev of the residuals), same units as y (cm3) • SE(slope) measures the variability in sample slopes from repeated samples, same units as slope (cm3/mm) • t-ratio measures how many standard errors observed slope is from 0, no units

  6. Exam 2 – Problem 5 • Response = yield, Explanatory – temperature and pressure, blocking = week • Randomized treatments within each week, helps control for any changes over time • Main effects: yield higher on average for 500o than 3000 (p-value < .001); yield higher on average for 200 psi than 100 psi (p-value < .001) • Interaction: bigger difference between 300o and 5000 when pressure is 200 (p-value = .007). • Blocking: moderately helpful (p-value = .065).

  7. Extra Credit • 95.32% of the variability in yield was explained by this model involving temperature, pressure, and weeks.

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