Exercise 8. 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. Is there a statistically significant relationship between the average birth weight and parity?
Researchers interested in the relationship between absenteeism from school and certain demographic characteristics of children collected data from randomly sam- pled students in rural New South Wales, Australia, in a particular school year. Below are three observations from this data set. Answer:Slope of eth Slope of sex 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.
Calculate the R2 and the adjusted R2. Note that there are observations in the data set. The table below shows the adjusted R-squared for the model as well as adjusted R-squared values for all models we evaluate in the first step of the backwards elimination process. Answer: No learner status should be removed from the model. On January 28, , a routine launch was anticipated for the Challenger space shuttle. Seventy-three seconds into the flight, disaster happened: the shuttle broke apart, killing all seven crew members on board.
An investigation into the cause of the disaster focused on a critical seal called an O-ring, and it is believed that damage to these O-rings during a shuttle launch may be related to the ambient temperature during the launch. The table below summarizes observational data on O-rings for 23 shuttle missions, where the mission order is based on the temperature at the time of the launch.
Temp gives the temperature in Fahrenheit, Damaged represents the number of damaged O-rings, and Undamaged represents the number of O-rings that were not damaged. ShuttleMission 1 2 3 4 5 6 7 8 9 10 11 12 Temperature 53 57 58 63 66 67 67 67 68 69 70 70 Damaged Undamaged ShuttleMission 13 14 15 16 17 18 19 20 21 22 23 Temperature 70 70 72 73 75 75 76 76 78 79 81 Damaged Undamaged 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. 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.
Add to Add to collection s Add to saved. Solution to Homework for Logistic Regression 1. Logistic regression for the combined data on incubation temperature and number of male and female turtles from eggs collected in Illinois is presented in Examples 5. The original data is given below. Temp This has a P-value of 0. Justify your answer statistically. The change in deviance is the same as in the combined data analysis; The data has been read in from a data frame and is stored in turtle.
Error t value Intercept There is also data on the relationship between the number of male turtles and incubation temperature for turtle eggs from New Mexico. The turtles are the same species as those from Illinois. You can either use the proportion male as the response with the number of turtles as weights or you can use cbind to create a two column response containing the number of males and number of females.
You do NOT have to use both ways, only one. The New Mexico data has fewer eggs and only three temperatures. The residual deviance is This corresponds to a P-value of 0. The change in deviance is This is over half a degree higher that the temperature for Illinois turtles. Make sure your plot has appropriate labels and a title. Temperature would be one variable. A second variable would be an indicator variable that indicated whether the proportion male was for Illinois turtles or New Mexico turtles.
A third variable would be a cross product of the temperature and the indicator. This also allows you to combine the data to get more degrees of freedom for the residual deviance. In the study, homes were selected and a coupon and advertising material for a particular product was sent to each home. The number of coupons redeemed was counted. Below are the data. Use this regression to estimate the proportion redeemed. Simple linear regression of observed proportions redeemed on the price reduction.
A note of caution, we are violating the assumptions for the t-test. However, the result is so extreme the violation is comparatively unimportant. The associated P-value would be virtually zero. The two equations using the logit transform logitslr and logistic are virtually the same in terms of the estimates.