8.2, 8.4, 8.8, 8.16, 8.18

Problem 8.2

  1. Weight = 120.07 - 1.93*parity

  2. The slope is how how every unit of parity affects weight. It is inversely related.

  3. There is no signfinicant relationship based on the t test.

Problem 8.4

  1. ‘Absenteeism = 18.93-9.11eth+3.1Sex+2.15lrn’

  2. For 9.11 change in eth we see a 1 unit change down in aboriginal

For 3.10 change in sex we see a 1 unit change up in aboriginal

For 2.15 change in lrn we see a 1 unit change up in aboriginal

  1. 3.1+2.15-2 = 3.25

  2. R^2= 1- (240.57)/264.17 = 0.0893

R2_adj= 1- (1-R^2)*(n-1)/(n-p-1)

= 1- (1-0.0893)*(146-1)/(146-3-1)

=0.070

Problem 8.8

Based on the model Adjusted R squares, I would get rid of the ‘No Ethnicity’ variable which, related to the sample size and degrees of freedom, doesn’t appear to be adding to the explainatory value of the model. The model has too many parameters.

Problem 8.16

  1. Heuristically I see that as temperature increases the likelihood of damaging an O ring also increases.

  2. The estimate of the slope parameter is negative, implying my heuristic above is correct. It also has a lower than 0.05 p value implying the relationship holds up statistically.

  3. log(p/(1-p)) = 11.663-.02162*Temp

  4. I absolutely conclucde that Temperature and O rings could be concerning. there is a signficant relationship between the variables implying that one should look into its causes (or possible co factor explainations)

Problem 8.18

t1=51
t2=53
t3=55

Model <- function(t)
{
  f <- 11.6630 - 0.2162 * t

  p <- exp(f) / (1 + exp(f))

  return (p)
}

Model(t1)
## [1] 0.6540297
Model(t2)
## [1] 0.5509228
Model(t3)
## [1] 0.4432456
temp <- seq(51, 82)

 setwd("C:/Users/sogde/Desktop")
 rate<-read.csv("Book2.csv")
head(rate)
##   Temp      Rate
## 1   53 0.7142857
## 2   57 0.1428571
## 3   58 0.1428571
## 4   63 0.1428571
## 5   66 0.0000000
## 6   67 0.0000000
df <- data.frame(Temperature=temp, Prob=Model(temp))

library(ggplot2)

ggplot(df) + geom_line(aes(x=Temperature, y=Prob )) + geom_point(data=rate, aes(x=Temp, y=Rate), colour="blue")

Concerns I have for this model are: 1) the point at temp=51 could be an outlier drasitcally affecting the shape of the model, 2) At each sample temperature we are given only ~7 chances for the event to fail.

However the independence condition is at least mostly met because the rockets thrusters are refurbrished every mission, however if there is an underlying flaw with a constant refurbrishing process then this does not hold true.