8.2)a) \(\hat{birth weight}\) = 120.07 - 1.93*parity

b) Children who are not first borns tend to be 1.93 ounces lighter than first born children.

c) Ho: \(\beta\) = 0
HA: \(\beta\) \(\neq\) 0
T = -1.62 and p value = 0.1052
Because the p value is greater than 0.05, we fail to reject the null hypothesis. Parity is not associated with a difference in brith weights.


8.4)a) \(\hat{days-absent}\) = 18.93 - 9.11eth + 3.10sex + 2.15lrn
b) A non-aboriginal student is likely to be absent 9.11 days less than an aboriginal student.
A male is likely to be absent 3.10 days more than a female.
A slow learner is likely to be absent 2.15 days more than an average learner.

c) \(\hat{days-absent}\) = 18.93 - 9.11(0) + 3.10(1) + 2.15(1)
\(\hat{days-absent}\) = 24.18 days
residual = 2 - 24.18 = -22.18 The model grossly over-estimated the number of days absent.

d) R^2 = 1 - 240.57/264.17 = 0.0893364
R^2 adj = 1 - 240.57/264.17 x (146-1)/(146-3-1) = .0701

8.8) Remove learner status

8.16) a) There appears to be a relationship between temperature and whether O-rings are damaged. The lower the temperature, the greater the likelihood of O rings being damaged. Below 57 degrees Farenheit, the likelihood of O-rings being damaged increase dramatically.

b) The intercept represents the value for O-ring damage when temperature is zero degrees Farenheit. The slope of -.2162 means that for every degree increase in temperature the likelihood of O-ring damage goes down by .2162.

c) ln (p/(1-p)) = 11.630 - 2.162Temperature

d) Ho - O-ring damage is independent of temperature.
HA- O-ring damage is dependent on temperature.
The p value for temperature is 0, which is less than 0.05. We reject the null hypothesis. O-ring damage is related to temperature.

8.18)a) T = 51 

calcp <- function(temp){
  logreg <- 11.630 - .2162*temp
  logreg <- exp(logreg)
  p <- logreg/(1 +  logreg)
  return (p)
  }

t51 <- calcp(51)
t53 <- calcp(53)
t55 <- calcp(55)
temp2 <- c(51, 53, 55)
prob2 <- c(t51, t53, t55)
model_prob <- data.frame(temp2, prob2, stringsAsFactors = FALSE)

The probability an O-ring will become damaged at 51 degrees is 0.6465252.
The probability an O-ring will become damaged at 53 degrees is 0.5427454.
The probability an O-ring will become damaged at 55 degrees is 0.4351179.

b)

temp <- c(53,57,58,63,66,67,67,67,68,69,70,70,70,70,72,73,75,75,76,76,78,79,81, temp2)
probdamage <- c(5/6, 1/6, 1/6,1/6,0,0,0,0,0,0,1/6,0,1/6,0,0,0,0,1/6,0,0,0,0,0, prob2)
oringdf <- data.frame(temp, probdamage, stringsAsFactors=FALSE)
plot(temp, probdamage, xlab="Temperature", ylab="Probability of O-ring damage")
xspline(model_prob, border='blue' )

  1. I am concerned that there is only one data point at 53 degrees and that data point plays a large role in determining the relationship between O-ring damage and temperature. I understand that since it is considered dangerous that this cannot be tested further, but it would have been helpful to have more data for O-ring damage at low temperatures. We need to assume that each outcome is independent of the other outcomes. This seems reasonable to me.