Stat 322 – Day 29

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?

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

Exam 2 – Problem 4 H 0 :   =20 vs. H a :   ≠20 t = ( – 20)/5.002 Degrees of freedom = n-2 = 5 Two-sided p-value Do not have evidence to doubt 20 cm 3 /mm

Exam 2 – Problem 4 s, measures the variability in the response variable at each x (standard dev of the residuals), same units as y (cm 3 ) SE(slope) measures the variability in sample slopes from repeated samples, same units as slope (cm 3 /mm) t-ratio measures how many standard errors observed slope is from 0, no units

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 500 o than (p-value <.001); yield higher on average for 200 psi than 100 psi (p-value <.001) Interaction: bigger difference between 300 o and when pressure is 200 (p-value =.007). Blocking: moderately helpful (p-value =.065).

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