Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 3.3, Problem 36PB
Midterm–final
a. Find the predicted final exam score for a student who has (i) midterm score = 100, (ii) midterm score = 50. Note that in each case the predicted final exam score regresses toward the mean of 75. (This is a property of the regression equation that is the origin of its name, as Chapter 12 will explain.)
b. Show that the correlation equals 0.60 and interpret it. (Hint: Use the relation between the slope and correlation.)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Data was collected from 60 students from the SAT, the average sat score was 909 with a standard deviation of 178. The average ACT score was 19 with a standard deviation of 3.5. The correlation between the two variables is 0.811.
a) To predict the SAT score from the ACT score, what is the equation of the leasts-square regression line.
b) What fraction of the variation in the values of the SAT scores is accounted for by the linear relationship between SAT and ACT scores. Explain
A pumpkin farmer wants to create a linear regression model to predict the circumference of a pumpkin (Y-variable) from its weight (X-variable). He samples 40 pumpkins from his pumpkin patch and the mean weight is 14 lbs with a standard deviation of 1 lb. The mean circumference is 50 inches with a standard deviation of 10 inches. The correlation between pumpkin weight and circumference is r = 0.50.
What is the slope of the linear regression model predicting circumference from weight?
7
1
5
3
A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking related to the risk of strokes. The data file “Stroke.xslx” includes a portion of the data from the study. The variable “Risk of Stroke” is measured as the percentage of risk (proportion times 100) that a person will have a stroke over the next 10-year period.
Regression Analysis As Image:
1) Based on the simple regression analysis output, write the estimated regression equation.
2) What is the correlation coefficient between Risk of Stroke and Age? How do you find i
Chapter 3 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 3.1 - Which is the response/explanatory variable? For...Ch. 3.1 - Sales and advertising Each month, the owner of...Ch. 3.1 - Does higher income make you happy? Every General...Ch. 3.1 - Diamonds The clarity and cut of a diamond are two...Ch. 3.1 - Alcohol and college students The Harvard School of...Ch. 3.1 - How to fight terrorism? A survey of 1000 adult...Ch. 3.1 - Heaven and hell Two questions on the General...Ch. 3.1 - Prob. 8PBCh. 3.1 - Gender gap in party ID In recent election years,...Ch. 3.1 - Use the GSS Go to the GSS website...
Ch. 3.2 - Used cars and direction of association For the 100...Ch. 3.2 - Broadband and GDP The Internet Use data file on...Ch. 3.2 - Prob. 13PBCh. 3.2 - Politics and newspaper reading For the FL Student...Ch. 3.2 - Prob. 15PBCh. 3.2 - Match the scatterplot with r Match the following...Ch. 3.2 - Prob. 17PBCh. 3.2 - Prob. 18PBCh. 3.2 - Prob. 19PBCh. 3.2 - Prob. 20PBCh. 3.2 - Prob. 21PBCh. 3.2 - Prob. 22PBCh. 3.2 - Prob. 23PBCh. 3.3 - Sketch plots of lines Identify the values of the...Ch. 3.3 - Prob. 25PBCh. 3.3 - Home selling prices The House Selling Prices FL...Ch. 3.3 - Prob. 27PBCh. 3.3 - Prob. 28PBCh. 3.3 - Prob. 29PBCh. 3.3 - Broadband subscribers and population The Internet...Ch. 3.3 - Prob. 31PBCh. 3.3 - Prob. 32PBCh. 3.3 - Regression between cereal sodium and sugar The...Ch. 3.3 - Prob. 34PBCh. 3.3 - Advertising and sales Each month, the owner of...Ch. 3.3 - Midtermfinal correlation For students who take...Ch. 3.3 - Predict final exam from midterm In an introductory...Ch. 3.3 - NL baseball Example 9 related y = team scoring...Ch. 3.3 - Study time and college GPA A graduate teaching...Ch. 3.3 - Oil and GDP An article in the September 16, 2006,...Ch. 3.3 - Mountain bikes revisited Is there a relationship...Ch. 3.3 - Mountain bike and suspension type Refer to the...Ch. 3.3 - Fuel Consumption Most cars are fuel efficient when...Ch. 3.4 - Extrapolating murder The SPSS figure shows the...Ch. 3.4 - Mens Olympic long jumps The Olympic winning mens...Ch. 3.4 - U.S. average annual temperatures Use the U.S....Ch. 3.4 - Murder and education Example 13 found the...Ch. 3.4 - Murder and poverty For Table 3.6, the regression...Ch. 3.4 - TV watching and the birth rate The figure shows...Ch. 3.4 - Looking for outliers Using software, analyze the...Ch. 3.4 - Regression between cereal sodium and sugar Let x =...Ch. 3.4 - Gestational period and life expectancy Does the...Ch. 3.4 - Antidrug campaigns An Associated Press story (June...Ch. 3.4 - Whats wrong with regression? Explain whats wrong...Ch. 3.4 - Education causes crime? The table shows a small...Ch. 3.4 - Death penalty and race The table shows results of...Ch. 3.4 - NAEP scores Eighth-grade math scores on the...Ch. 3.4 - Age a confounder? A study observes that the...Ch. 3 - Choose explanatory and response For the following...Ch. 3 - Graphing data For each case in the previous...Ch. 3 - Life after death for males and females In a recent...Ch. 3 - God and happiness Go to the GSS website...Ch. 3 - Degrees and income The mean annual salaries earned...Ch. 3 - Bacteria in ground turkey Consumer Reports...Ch. 3 - Women managers in the work force The following...Ch. 3 - RateMyProfessor.com The website RateMyProfessors....Ch. 3 - Women in government and economic life The OECD...Ch. 3 - African droughts and dust Is there a relationship...Ch. 3 - Crime rate and urbanization For the data in...Ch. 3 - Gestational period and life expectancy revisited...Ch. 3 - Height and paycheck The headline of an article in...Ch. 3 - Predicting college GPA An admissions officer...Ch. 3 - College GPA = high school GPA Refer to the...Ch. 3 - Whats a college degree worth? In 2002, a census...Ch. 3 - Care Weight and gas hogs: The table shows a short...Ch. 3 - Predicting Internet use from cell phone use We now...Ch. 3 - Income depends on education? For a study of...Ch. 3 - Fertility and GDP Refer to the Human Development...Ch. 3 - Women working and birth rate Using data from...Ch. 3 - Education and income The regression equation for a...Ch. 3 - Income in euros Refer to the previous exercise....Ch. 3 - Changing units for cereal data Refer to the Cereal...Ch. 3 - Murder and single-parent families For Table 3.6 on...Ch. 3 - Violent crime and college education For the U.S....Ch. 3 - Violent crime and high school education Repeat the...Ch. 3 - Crime and urbanization For the U.S. Statewide...Ch. 3 - High school graduation rates and health insurance...Ch. 3 - Womens Olympic high jumps Example 11 discussed how...Ch. 3 - Income and height A survey of adults revealed a...Ch. 3 - More TV watching goes with fewer babies? For...Ch. 3 - More sleep causes death? An Associated Press story...Ch. 3 - Ask Marilyn Marilyn vos Savant writes a column for...Ch. 3 - Time studying and GPA Is there a relationship...Ch. 3 - Warming in Newnan, Georgia Access the Newnan GA...Ch. 3 - Fluoride and AIDS An Associated Press story...Ch. 3 - Fish fights Alzheimers An AP story (July 22, 2003)...Ch. 3 - Dogs make you healthier A study published in the...Ch. 3 - Multiple choice: Correlate GPA and GRE In a study...Ch. 3 - Multiple choice: Properties of r Which of the...Ch. 3 - Multiple choice: Interpreting r One can interpret...Ch. 3 - Multiple choice: Correct statement about r Which...Ch. 3 - Multiple choice: Describing association between...Ch. 3 - Multiple choice: Slope and correlation The slope...Ch. 3 - Multiple choice: Interpretation of r2 An r2...Ch. 3 - True or false The variables y = annual income...Ch. 3 - Correlation doesnt depend on units Suppose you...Ch. 3 - When correlation = slope Consider the formula...Ch. 3 - Center of the data Consider the formula a=ybx for...Ch. 3 - Final exam regresses toward mean of midterm Let y...Ch. 3 - Activity: Guess the correlation The Guess the...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- What is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forwardSuppose the athletic director at a university would like to develop a regression model to predict the point differential for games played by the men's basketball team. A point differential is the difference between the final points scored by two competing teams. A positive differential is a win, and a negative differential is a loss. For a random sample of games, the point differential was calculated, along with the number of assists, rebounds, turnovers, and personal fouls. Use the data in the accompanying table attached below to complete parts a through e below. Assume a = 0.05. a) Using technology, construct a regression model using all three independent variables. y = __ + (_)x1 + (_)x2 + (_)x3 + (_)x4 b) Test the significance of each independent variable using a= 0.10. c) interpret the p-value for each independent variable. d) Construxt a 90% confidence interval for the regression coefficients for each independent variable and interpret the meaning. e) Using the results from…arrow_forwardThe correlation between first year college GPA and high school GPA is 0.683. If a simple linear regression was conducted to predict first year college GPA from high school GPA what does the correlation tell us about the fit of the model?arrow_forward
- A linear relationship exists between two variables x and y. The correlation coefficient was calculated for the sample data and is equal to -0.93. Using the estimated regression equation, a straight line that will best fit the data points can be drawn through the points on the scattergram.The line slopes downward from left to right and the points are scattered close to the line. True or falsearrow_forwardThe correlation coefficient between midterm and final scores in a large statistics class is r=0.6. A scatterplot of the two variables is football shaped. A particular student has a midterm score that is 0.5 SDs below the average midterm score of all students. Using regression, we would predict that the student's final score is _________ SDs _________ the average final score of all students and therefore at the _________ percentile of final scores of all students.arrow_forwardWrite out the regression equation based on the output. What happens to exam performance with every increase in exam anxiety and what do you notice about the standardized regression coefficient (Beta) and the correlation?arrow_forward
- Find correlation coefficient between the exchange and expenditure from the datagiven below: Obtain the regression equation of exchange on expenditure expenses and find out theexpected exchange of a firm when expenditure is Rs. 25 lakhs. Also find coefficientof determination and interpret your result.arrow_forwarda. Determine the correlation coefficient r between the two variables. b. Determine the slope coefficient β1 for the regression of marks on study time. c. What will be the expected marks of a student who studied for 33 hours?arrow_forwardDevelop a simple linear regression equation for starting salaries using an independent variable that has the closest relationship with the salaries. Explain how you chose this variable.arrow_forward
- Comoute the least-squres regression equation for predicting y from x given the following summary statistics.arrow_forwardA group of scientists are interested in finding out whether the days of rainfall during the dry season could predict the magnitude of butterfly migration in the local area during wet season. Every year for twenty years, they count the total days of rainfall during the dry season preceding the migration and measure the number of butterflies migrating in the following wet season. Which type of statistical test should they use to analyze their data? (pearson's r correlation OR, simple regression equation)arrow_forwarddefine and state the difference between the three terms association, correlation and causation. find the regression line between the height of the strawberry plant and the water it gets per day and interpret the intercept and slope coefficients. find a 95% confidence interval around the plant estimate of the slope parameter from your model.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
The Shape of Data: Distributions: Crash Course Statistics #7; Author: CrashCourse;https://www.youtube.com/watch?v=bPFNxD3Yg6U;License: Standard YouTube License, CC-BY
Shape, Center, and Spread - Module 20.2 (Part 1); Author: Mrmathblog;https://www.youtube.com/watch?v=COaid7O_Gag;License: Standard YouTube License, CC-BY
Shape, Center and Spread; Author: Emily Murdock;https://www.youtube.com/watch?v=_YyW0DSCzpM;License: Standard Youtube License