Data606-Homework8

Problem 8:2

a)bw=120.07-1.93p
b)In this case, there are only two possibilities. One is a first born, in which case the prediction is 120.07 (ounces?) Subsequeant children have a predicted weight of 118.77 ounces.
c)There is not a statistically significant relationship, as the t-score is greater than .1.

Problem 8:4

a) absenteeism = 18.93 - 9.11(eth) + 3.10(sex) = 2.15(lrn)
b) The slope coefficients mean that an aboriginal student is likely to be absent 9.11 more days, a male is likely to miss 3.11 more days and a “slow learner” was likely to miss 2.15 more days.
c) An aboriginal, male, “slow learner” who missed 2 days, accounts for a residual of -22.18.
d) The R² is \(1-\frac{240.57}{264.17}=.070097\)
The adjusted R² is \(1-\frac{240.57}{264.17}*\frac{n-1}{n-k-1}=.089336\)

Problem 8:8

The ethnicity variability, with the lowest adjusted R², should be removed first.

Problem 8:16

a) Half of the observed damaged o-rings are from the 2 coldest launches. All of the 4 coldest launches produced a damaged o-ring.
b) There is a row for the intercept and for the temperature. The first column is the fitted values. The next is the standard error, which is a measure of variability. The next, the z-value, indicates the likelihood of experiencing the data, given there was no relationship. The last is the amount of probability in the tail, past the z-score.
c) \(\small ln\frac{\pi}{1-\pi} = 11.663 - .2162(temp)\)
d) The null hypothesis is rejected at a level of .01. There is a statistically significant relationship between temperature and o-ring damage.

Problem 8:18

a) For 51 degrees, the prediction is 0.6540297.
For 53 degrees, the prediction is 0.5509228.
For 55 degrees, the prediction is 0.4432456.

b)

c) It is appropriate to use a logistic regression when our response variable has 2 categories. The original data had one point that experienced 5 failures. Using a logit model lowered the leverage of that first point (so it might be stronger). Our model could be further checked if we looked AIC, BIC, chi-square or cross-validation tests, among others.