Chapter 12, Problem 12.78CRP

A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?

Suppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading.  Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂  when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…

An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second city

Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is Bags = -151.05 +2.65Temp. On one of the observed days, the temperature was 82 °F and 68 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line, Bags, when the temperature is (82\ \text (°F. J\\) Enter your answer as a whole number, rounding if necessary. Bags = 1.11 residual Incorrect Using the predicted value you just found, compute the residual at this temperature. 1.11 Incorrect ice bags ice bags

The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. y = x+ (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y =x+ Number of Number of (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Number of Male Fatal Number of Female Fatal Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if…

Compute the least-squares regression line for predicting the 2012 budget from the 2006 budget. Round the slope and y- intercept to at least four decimal places.

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. ..... (a) The coefficient of determination of the expanded data set is R = %. Weight (pounds), x Miles per (Round to one decimal place as needed.) Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27

Suppose the manager of a gas station monitors how many bags of ice he sells daily along with recording the highest temperature each day during the summer. The data are plotted with temperature, in degrees Fahrenheit (°F), as the explanatory variable and the number of ice bags sold that day as the response variable. The least squares regression (LSR) line for the data is =-114.05+2.17X. On one of the observed days, the temperature was 85 °F and 66 bags of ice were sold. The number of bags of ice predicted to be sold by the LSR line, y, when the temperature is 85 °F is 70. Using the predicted value, compute the residual at this temperature. Answer:

The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x+ 41.337. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Click the icon to view the data table. Data Table ..... Weight (pounds), x Miles per (a) The coefficient of determination of the expanded data set is R = %. Gallon, y (Round to one decimal place as needed.) Car 1 3,771 22 Car 2 ,990 19 Car 3 3,534 20 Car 4 3,172 24 Car 5 2,579 27 Car 6 3,730 20 Car 7 2,605 25 Car 8 3,777 19 Car 9 3,308 19 Car 10 2,997 26 Car 11 2,751 27