Mileage Data Analysis(cont Variations of the individual measurements about this estimate are The sample mean of these variations is ∑(d-a)=0 So the estimate is unbiased
Mileage Data Analysis (cont.) • Variations of the individual measurements, about this estimate are ei = di − dˆ • The sample mean of these variations is n n 1 n eˆ = ∑ ei = 1 ∑ ( di − dˆ) = 0 i =1 n i =1 • So the estimate is unbiased
Mileage Data Analysis(cont) Assuming the variations are statistically independent we can also compute the sample standard deviation of these variations as e. =.026miles 1
Mileage Data Analysis (cont.) • Assuming the variations are statistically independent we can also compute the sample standard deviation of these variations as n n σˆ = 1 ∑( di − dˆ )2 = (n 1 −1) ∑ ei 2 = .026 mile s (n −1) i =1 i =1
Mileage Data Analysis(cont) Since my experiment consisted of a number of independent trials it is reasonable to assume that the route distance, as determined by my measurements, is gaussian probability density of 954 confidence route distance 7.9口 7.95 8.05口 8.15口 mues
Mileage Data Analysis (cont.) • Since my experiment consisted of a number of independent trials it is reasonable to assume that the route distance, as determined by my measurements, is gaussian probability density of route distance 0 2 4 6 8 10 12 14 16 7.85 7.9 7.95 8 8.05 8.1 8.15 .954 confidence miles
Linear system models The system model for my experiment assumed that the route distance is constant In many instances the system model is not constant but is a linear function Define a linear system model as t cx where x= independent variable y≡ dependent variable
Linear System Models • The system model for my experiment assumed that the route distance is constant • In many instances the system model is not constant but is a linear function • Define a linear system model as y = c0 + c1x where x ≡ independent variable y ≡ dependent variable