Chapter 8 - Multiple and Logistic Regression Practice: 8.1, 8.3, 8.7, 8.15, 8.17 Graded: 8.2, 8.4, 8.8, 8.16, 8.18

8.2 Baby weights, Part II.

Exercise 8.1 introduces a data set on birth weight of babies. Another variable we consider is parity, which is 0 if the child is the first born, and 1 otherwise. The summary table below shows the results of a linear regression model for predicting the average birth weight of babies, measured in ounces, from parity.

  1. Write the equation of the regression line. y = 120.07 -1.93 * parity

  2. Interpret the slope in this context, and calculate the predicted birth weight of first borns and others. For each parity the weight of the child is decreased by 1.93.

  3. Is there a statistically significant relationship between the average birth weight and parity? No, the P value for parity is over 10%.

8.4 Absenteeism, Part I.

  1. Write the equation of the regression line. y=18.93 -9.11eth + 3.10sex + 2.15*lrn

  2. Interpret each one of the slopes in this context. The model predicts a 9.11 decrease for in chances absenteeism if student is aborginal, all else held constant. The model predicts a 3.10 increase for in chances absenteeism if student is male, all else held constant. The model predicts a 2.15 increase for in chances absenteeism if student is considered a slow learner, all else held constant.

  3. Calculate the residual for the first observation in the data set: a student who is aboriginal, male, a slow learner, and missed 2 days of school.

18.93-9.11*0 + 3.10*1 + 2.15*1
## [1] 24.18

2-24.18 = 22.18 The model under-predicts by 22.18

  1. The variance of the residuals is 240.57, and the variance of the number of absent days for all students in the data set is 264.17. Calculate the R2 and the adjusted R2. Note that there are 146 observations in the data set.

R2 = 1 - var(ei)/var(yi) R2 = 1- 240.57/264.17 R2 adjusted = 1- var(ei)/var(yi) * n-1/n-k-1 R2 adjusted = 1- 240.57/264.17 * 146-1/146-3-1

1- 240.57/264.17
## [1] 0.08933641
1- (240.57/264.17) * (146-1)/(146-3-1)
## [1] 0.07009704

8.8 Absenteeism, Part II.

No Learner Status should be removed first since it has the highest adjusted R^2.

8.16 Challenger disaster, Part I.

  1. Each column of the table above represents a different shuttle mission. Examine these data and describe what you observe with respect to the relationship between temperatures and damaged O-rings.

  2. Failures have been coded as 1 for a damaged O-ring and 0 for an undamaged O-ring, and a logistic regression model was fit to these data. A summary of this model is given below. Describe the key components of this summary table in words.

  3. Write out the logistic model using the point estimates of the model parameters.

  4. Based on the model, do you think concerns regarding O-rings are justi ed? Explain.

8.18 Challenger disaster, Part II.

The data provided in the previous exercise are shown in the plot. The logistic model t to these data may be written as

log(p/1-p) = 11.6630 - 0.2162 * Temperature

where ^p is the model-estimated probability that an O-ring will become damaged. Use the model to calculate the probability that an O-ring will become damaged at each of the following ambient temperatures: 51, 53, and 55 degrees Fahrenheit. The model-estimated probabilities for several additional ambient temperatures are provided below, where subscripts indicate the temperature: ^p57 = 0:341 ^p59 = 0:251 ^p61 = 0:179 ^p63 = 0:124 ^p65 = 0:084 ^p67 = 0:056 ^p69 = 0:037 ^p71 = 0:024

  1. Add the model-estimated probabilities from part (a) on the plot, then connect these dots using a smooth curve to represent the model-estimated probabilities.

  2. Describe any concerns you may have regarding applying logistic regression in this application, and note any assumptions that are required to accept the model’s validity.