In an experiment to determine the factors affecting tensile strength in steel plates, the tensile strength (in kg/mm2 ), the manganese content (in parts per thousand), and the thickness (in mm) were measured for a sample of 20 plates. The following MINITAB output presents the results of fitting the model Tensile strength = 0 + 1 Manganese +B2 thickness The regression equation is Strength = 26.641 + 3.3201 Manganese 0.4249 Thickness Predictor Coef StDev T P Constant 26.641 2.72340 9.78 0.000 Manganese 3.3201 0.33198 10.00 0.000 Thickness 0.4249 0.12606 3.37 0.004 S = 0.8228 R-Sq = 86.2% R-Sq(adj) = 84.6% Analysis of Variance Source DF SS MS F P Regression 2 72.01 36.005 53.19 0.000 Residual Error 17 11.508 0.6769 Total 19 83.517 a. Predict the strength for a specimen that is 10 mm thick and contains 8.2 ppt manganese. b. If two specimens have the same thickness, and one contains 10 ppt more manganese, by how much would you predict their strengths to differ? c. If two specimens have the same proportion of manganese, and one is 5 mm thicker than the other, by how much would you predict their strengths to differ?
Week 2 Being mathematically precise about describing quantitative value distribution Measuring center: MEAN - Mean: the arithmetic average The sample mean, which is a statistic, is denoted by X´ (“ex- bar”): X +X +…+X ∑ X X= 1 2 = i n n where n is the sample size - The population mean, which is a parameter, is denoted by μ (“mu”): x1+x 2…+x N ∑ xi μ= N = N where N is the population size - The mean is sensitive/nonresistant to outliers, it is pulled towards the tail in a skewed distribution MEDIAN - The mean cannot be very useful when you have big outlier(s), so we use the median to measure center - To find the median 1. Reorder data value from smallest to lar