Introductory Statistics
3rd Edition
ISBN: 9780135188927
Author: Gould, Robert, Ryan, Colleen N. (colleen Nooter)
Publisher: Pearson,
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Textbook Question
Chapter 4, Problem 68SE
Weight of Trash and Household Size Data were collected that included information on the weight of the trash (in pounds) on the street for one week and the number of people who live in the house. The following figure shows a
a. Is the trend positive or negative? What does that mean?
b. Now calculate the
c. Report the slope. For each additional person in the house, there are, on average, how many additional pounds of trash?
d. Either report the intercept or explain why it is not appropriate to interpret it.
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3. Bayesian Inference – Updating Beliefs
A medical test for a rare disease has the following characteristics:
Sensitivity (true positive rate): 99%
Specificity (true negative rate): 98%
The disease occurs in 0.5% of the population.
A patient receives a positive test result.
Questions:
a) Define the relevant events and use Bayes’ Theorem to compute the probability that the patient actually has the disease.b) Explain why the result might seem counterintuitive, despite the high sensitivity and specificity.c) Discuss how prior probabilities influence posterior beliefs in Bayesian inference.d) Suppose a second, independent test with the same accuracy is conducted and is also positive. Update the probability that the patient has the disease.
4. Linear Regression - Model Assumptions and Interpretation
A real estate analyst is studying how house prices (Y) are related to house size in square feet (X). A simple
linear regression model is proposed:
The analyst fits the model and obtains:
•
Ŷ50,000+150X
YBoB₁X + €
•
R² = 0.76
• Residuals show a fan-shaped pattern when plotted against fitted values.
Questions:
a) Interpret the slope coefficient in context.
b) Explain what the R² value tells us about the model's performance.
c) Based on the residual pattern, what regression assumption is likely violated? What might be the
consequence?
d) Suggest at least two remedies to improve the model, based on the residual analysis.
Chapter 4 Solutions
Introductory Statistics
Ch. 4 - GPA Predictors The scatterplots show SAT scores...Ch. 4 - Salary and Employment The first graph shows the...Ch. 4 - Age and Credits The scatterplot below shows data...Ch. 4 - Age and GPA The scatterplot shows data on age and...Ch. 4 - Credits and GPA (Example 1) The scatterplot shows...Ch. 4 - Salary and Education The scatterplot shows data on...Ch. 4 - Sisters and Brothers The scatterplot shows the...Ch. 4 - House Price and Area Describe the trend in the...Ch. 4 - Work and TV The scatterplot shows the number of...Ch. 4 - Work and Sleep The scatterplot shows the number of...
Ch. 4 - Age and Sleep The scatterplot shows the age and...Ch. 4 - Height and Weight for Women The figure shows a...Ch. 4 - College Tuition and ACT a. The first scatterplot...Ch. 4 - Ages of Women Who Give Birth The figure shows a...Ch. 4 - Law School The scatterplot shows the LSAT (Law...Ch. 4 - Medical School The scatterplot shows the...Ch. 4 - Matching Pick the letter of the graph that goes...Ch. 4 - Matching Pick the letter of the graph that goes...Ch. 4 - Matching Match each of the following correlations...Ch. 4 - Matching Match each of the following correlations...Ch. 4 - Airline Tickets (Example 2) The distance (in...Ch. 4 - Train Tickets The table for part (a) shows...Ch. 4 - SAT and GPA In Exercise 4.1 there is a graph of...Ch. 4 - House Price The correlation between house price...Ch. 4 - Rate My Professor Seth Wagerman, a former...Ch. 4 - Cousins Five people were asked how many female...Ch. 4 - GPA and Gym Use USA Today College published an...Ch. 4 - Education and Life Expectancy United Press...Ch. 4 - Salaries of College Graduates (Example 3) The...Ch. 4 - Mother and Daughter Heights The graph shows the...Ch. 4 - Median Weekly Earning by Gender The scatterplot...Ch. 4 - Home Prices and Size The scatterplot shows the...Ch. 4 - Height and Arm Span for Women (Example 4) TI-84...Ch. 4 - Hand and Foot Length for Women The computer output...Ch. 4 - Height and Arm Span for Men (Example 5)...Ch. 4 - Hand Length and Foot Length for Men Measurements...Ch. 4 - Comparing Correlation for Arm Span and Height The...Ch. 4 - Age and Weight for Men and Women The scatterplot...Ch. 4 - Singles and Doubles Winning Percentage The...Ch. 4 - Seesaw The figure shows a scatterplot of the...Ch. 4 - Choosing the Predictor and Response Variables...Ch. 4 - Choosing the Predictor and the Response Variable...Ch. 4 - Percentage of Smoke-Free Homes and Percentage of...Ch. 4 - Effect of Adult Smoking on High School Student...Ch. 4 - Car Insurance and Age The following graph shows...Ch. 4 - Life Insurance and Age The graph shows the monthly...Ch. 4 - How Is the Time of a Flight Related to the...Ch. 4 - Distance and Train Ticket Price The following...Ch. 4 - Do States with Higher Populations Have More...Ch. 4 - Movie Ratings The following table give the Rotten...Ch. 4 - Pitchers The table shows the Earned Run Average...Ch. 4 - Text Messages The following table shows the number...Ch. 4 - Answer the questions using complete sentences. a....Ch. 4 - Answer the questions using complete sentences. a....Ch. 4 - If there is a positive correlation between number...Ch. 4 - Suppose that the growth rate of children looks...Ch. 4 - Coefficient of Determination If the correlation...Ch. 4 - Coefficient of Determination Does a correlation of...Ch. 4 - Investing Some investors use a technique called...Ch. 4 - Blood Pressure Suppose a doctor telephones those...Ch. 4 - Salary and Year of Employment (Example 8) The...Ch. 4 - MPG: Highway and City The following figure shows...Ch. 4 - Cost of Turkeys The following table shows the...Ch. 4 - Wine Calories The table shows the calories in a...Ch. 4 - Teacher Pay and Expenditure Per Student (Example...Ch. 4 - Teacher Pay and High School Graduation Rates The...Ch. 4 - Does Having a Job Affect Students’ Grades?...Ch. 4 - Weight of Trash and Household Size Data were...Ch. 4 - Predicting Home Runs Data on the number of home...Ch. 4 - Predicting 3-Point Baskets Data on the 3-point...Ch. 4 - 4th-Grade Reading and Math Scores Data from the...Ch. 4 - SAT Scores The following table shows the average...Ch. 4 - Test Scores Assume that in a political science...Ch. 4 - Test Scores Assume that in a sociology class, the...Ch. 4 - Heights and Weights of People The following table...Ch. 4 - Heights and Weights of Men The table shows the...Ch. 4 - Prob. 77CRECh. 4 - Granola Bars The following table shows the fat...Ch. 4 - Shoe Size and Height The scatterplot shows the...Ch. 4 - Age and Sleep The following scatterplot shows the...Ch. 4 - Age and Weight The following scatterplot shows the...Ch. 4 - Heights and Test Scores a. The following figure...Ch. 4 - Law School Selectivity and Employment The...Ch. 4 - Prob. 84CRECh. 4 - Prob. 87CRECh. 4 - Fuel-Efficient Cars The following table gives the...Ch. 4 - Tall Buildings The following scatterplot shows...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - For 4.91 through 4.94 show your points in a rough...Ch. 4 - The following figure shows a scatterplot of the...Ch. 4 - Wages and Education The figure shows a scatterplot...Ch. 4 - Do Students Taking More Units Study More Hours?...Ch. 4 - Hours of Exercise and Hours of Homework The...Ch. 4 - Children’s Ages and Heights The following figure...Ch. 4 - Blackjack Tips The following figure shows the...Ch. 4 - Decrease in Cholesterol A doctor is studying...Ch. 4 - Prob. 102CRE
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