STAT 4220

Homework 2

Report

Problem 1.22:

a) Yˆ = 168.6 + 2.03X
b) Yˆh = 168.6 + 2.03(40) = 168.6 + 81.2 = 249.8 c) 2.03

The population study is plastic hardness. The X is the elapsed time in hours and the Y is the hardness in Brinell units. The minimum unit was 196 with maximum to 253. The hours were 16 minimum and
40 maximum. The mean (average) was 225.6 for units and 28 for hours. The median was 226.5 units and 28 hours. The standard deviation of units with hour was 173.6. There was small variance large bias.

Problem 1.28:

a) a)Yˆ = 20517.6 + (-170.58)X
No this equation does not fit well because there is not a line. b) 1)-170.58
2) Yˆh = 6871.2
3) ε10 = 1401.57
4) MSE= 5552112

The population was crime rates. The x is the percentage of the individuals in the county having at least high-school diploma and Y is the crime rate. The maximum percentage was 91 with the lowest 61. The crime rate was the maximum 14016 with the lowest 2105. The mean (average) was 7111 crime rate and
78.6 percent. The median was 79 percent and 6930 crime rate. The standard deviation of crime rate and percent was -6601.54. There was a Large variance small bias.

Problem 1.31:

In this problem the error will not include batch to batch variability and there will be a smaller variance from the original experiment. When you are going to use different batches there will not be a way to evaluate your results from the original experiment and the results there going to be different. Because the measurements are all made in the same batch maybe there is going to be correlated over time.

Problem 1.33:

Q=Σ(Yi-β0)2  dQ/dβ0 = -2 Σ (Υi-β0)  Σ (Υi-β0) =0

Ε{b0} = E{Y} = 1/nΣ Ε{Υi} = 1/nΣ β0 =