An article in Wood Science and Technology [“Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep and Time to Failure” (1981, Vol. 15, pp. 125–144)] reported a study of the deflection (mm) of particleboard from stress levels of relative humidity. Assume that the two variables are related according to the simple linear regression model. The data follow:
(a) Calculate the least square estimates of the slope and intercept. What is the estimate of σ2? Graph the regression model and the data.
(b) Find the estimate of the mean deflection if the stress level can be limited to 65%.
(c) Estimate the change in the mean deflection associated with a 5% increment in stress level.
(d) To decrease the mean deflection by one millimeter, how much increase in stress level must be generated?
(e) Given that the stress level is 68%, find the fitted value of deflection and the corresponding residual.
Key Vocab Tips Chapter 15: Frequencies and Distributions Distribution of Large data: frequency the value occurs - Helps to better understand frequency in large data set - Estimates distribution shape or population from sample distribution shape Frequency Table Normal Distribution - Large sample from the population should be normally distributed - Bell Shaped Curve: Gaussian curves > Gauss created complicated stats Skewed Distribution - Negative: easy test; values cluster at top *ceiling effect* - Positive: Hard test; values cluster at bottom *floor effect* - Kurtosis: shape of curve How to remember positive and negative skewed dis