Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.3, Problem 1AYU
Suppose a least-squares regression line is given by
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A regression was run to determine if there is a relationship between the happiness index (y) and lifeexpectancy in years of a given country (x). The results of the regression were: y^=a+bx ; a=-0.423 ,b=0.07
a. Write the equation of the Least Squares Regression line.b. Find the value for the correlation coefficient, r?c. If a country increases its life expectancy, the happiness index will Increase or decrease ( circleone)d. If the life expectancy is increased by 1 year in a certain country, how much will the happinessindex change? Round to two decimal places.e. Use the regression line to predict the happiness index of a country with a life expectancy of 85years. Round to two decimal places.-
A regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The least squares regression line is weight = -5.94 + 0.1875 length.
ย
Explain in words what this model means (slop and intercept)
The new- born boy was 48 cm long, what is the predicted weight of this boy?
It is known that the boy is weighed 3 kg. what was his residual? What does that say about him?
Identify two different conditions under which the regression line should not be used to make predictions.
Chapter 12 Solutions
Fundamentals of Statistics (5th Edition)
Ch. 12.1 - True or False: The shape of the chi-square...Ch. 12.1 - A _____ test is an inferential procedure used to...Ch. 12.1 - Suppose there are n independent trials of an...Ch. 12.1 - What are the two requirements that must be...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - In Problems 5 and 6, determine the expected counts...Ch. 12.1 - Prob. 7AYUCh. 12.1 - Prob. 8AYUCh. 12.1 - In Problems 710, determine (a) the 2 test...Ch. 12.1 - In Problems 710, determine (a) the 2 test...
Ch. 12.1 - Applying the Concepts 11. NW Plain MMs According...Ch. 12.1 - Peanut MMs According to the manufacturer of MMs,...Ch. 12.1 - Prob. 13AYUCh. 12.1 - Prob. 14AYUCh. 12.1 - Always Wear a Helmet The National Highway Traffic...Ch. 12.1 - Religion in Congress Is the religious make-up of...Ch. 12.1 - Does It Matter Where I Sit? Does the location of...Ch. 12.1 - Racial Profiling On January 1, 2004, it became...Ch. 12.1 - Prob. 19AYUCh. 12.1 - Prob. 20AYUCh. 12.1 - Prob. 21AYUCh. 12.1 - Is the Die Loaded? A player in a craps game...Ch. 12.1 - Grade Distributions At Joliet Junior College, the...Ch. 12.1 - Population Shift An urban economist wonders if the...Ch. 12.1 - Prob. 25AYUCh. 12.1 - Living Alone? In 2000, 25.8% of Americans 15 years...Ch. 12.1 - Putting It Together: The V-2 Rocket in London In...Ch. 12.1 - Putting It Together: Weldons Dice On February 2,...Ch. 12.1 - Buying a New Car How much does the typical person...Ch. 12.1 - Why is goodness of fit a good choice for the title...Ch. 12.1 - Explain why chi-square goodness-of-fit tests are...Ch. 12.1 - Prob. 32AYUCh. 12.2 - True or False: The expected frequencies in a...Ch. 12.2 - In a chi-square test for ____ of proportions, we...Ch. 12.2 - The following table contains observed values and...Ch. 12.2 - The table in the next column contains observed...Ch. 12.2 - Prob. 5AYUCh. 12.2 - Prob. 6AYUCh. 12.2 - NW Family Structure and Sexual Activity A...Ch. 12.2 - Prenatal Care An obstetrician wants to learn...Ch. 12.2 - Health and Happiness Are health and happiness...Ch. 12.2 - Health and Education Does amount of education play...Ch. 12.2 - Social Well-Being and Obesity The Gallup...Ch. 12.2 - Profile of Smokers The following data represent...Ch. 12.2 - Efficacy of e-Cigs Do electronic cigarettes assist...Ch. 12.2 - Celebrex Celebrex, a drug manufactured by Pfizer,...Ch. 12.2 - NW Whats in a Word? In a recent survey conducted...Ch. 12.2 - Whats in a Word? Part II In a recent survey...Ch. 12.2 - Dropping a Course A survey was conducted at a...Ch. 12.2 - Prob. 18AYUCh. 12.2 - Prob. 19AYUCh. 12.2 - Prob. 20AYUCh. 12.2 - Putting It Together: Women, Aspirin, and Heart...Ch. 12.2 - Homeruns Go to...Ch. 12.2 - Explain the differences between the chi-square...Ch. 12.2 - Why does the test for homogeneity follow the same...Ch. 12.3 - Suppose a least-squares regression line is given...Ch. 12.3 - Prob. 2AYUCh. 12.3 - Prob. 3AYUCh. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - Prob. 8AYUCh. 12.3 - Prob. 9AYUCh. 12.3 - Prob. 10AYUCh. 12.3 - An Unhealthy Commute The following data represent...Ch. 12.3 - Credit Scores An economist wants to determine the...Ch. 12.3 - Height versus Head Circumference A pediatrician...Ch. 12.3 - Hurricanes The data in the next column represent...Ch. 12.3 - Concrete As concrete cures, it gains strength. The...Ch. 12.3 - Tar and Nicotine Every year the Federal Trade...Ch. 12.3 - Invest in Education Go to...Ch. 12.3 - American Black Bears In 1969, Dr. Michael R....Ch. 12.3 - CEO Performance (Refer to Problem 31 in Section...Ch. 12.3 - Bear Markets (Refer to Problem 32. Section 4.1) A...Ch. 12.3 - Age versus HDL Cholesterol A doctor wanted to...Ch. 12.3 - Prob. 22AYUCh. 12.3 - Influential Observations Zillow.com is a site that...Ch. 12.3 - Why is it important to perform graphical as well...Ch. 12.3 - Prob. 25AYUCh. 12.3 - Why is it desirable to have the explanatory...Ch. 12.4 - Intervals constructed about the predicted value of...Ch. 12.4 - Prob. 2AYUCh. 12.4 - Prob. 3AYUCh. 12.4 - Using the sample data from Problem 6 in Section...Ch. 12.4 - Prob. 5AYUCh. 12.4 - Prob. 6AYUCh. 12.4 - Prob. 7AYUCh. 12.4 - Prob. 8AYUCh. 12.4 - Prob. 9AYUCh. 12.4 - Prob. 10AYUCh. 12.4 - Prob. 11AYUCh. 12.4 - Tar and Nicotine Use the results of Problem 16 in...Ch. 12.4 - Prob. 13AYUCh. 12.4 - Prob. 14AYUCh. 12.4 - CEO Performance Use the results of Problem 19 from...Ch. 12.4 - Prob. 16AYUCh. 12.4 - Prob. 17AYUCh. 12 - Roulette Wheel A pit boss suspects that a roulette...Ch. 12 - Prob. 2RECh. 12 - Titanic With 20% of men, 74% of women, and 52% of...Ch. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Seat Choice and GPA A biology professor wants to...Ch. 12 - Apartments The following data represent the square...Ch. 12 - Calories versus Sugar The following data represent...Ch. 12 - A pit boss is concerned that a pair of dice being...Ch. 12 - Prob. 2CTCh. 12 - The Harris Poll asked a random sample of adult...Ch. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Crickets make a chirping noise by sliding their...Ch. 12 - The following data represent the height (inches)...Ch. 12 - A researcher believes that as age increases, the...Ch. 12 - CASE STUDY Feeling Lucky? Well, Are You? In fiscal...
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- Write down the formula of least square regression line?arrow_forwardSuppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line whereย ?Xย is the age of the crab in months andย ?หY^ย is the predicted value ofย ?Y, the size of the male crab inย cm. ?ห=8.2052+0.5693?Y^=8.2052+0.5693X ย What is the value ofย ?หY^ย when a male crab is 21.7865 months old? Provide your answer with precision to two decimalย places. ?ห= ย ย Interpret the value of ?ห. The value of ?ห is the predicted number of crabs out of the 1,000 crabs collected that will be 21.7865 monthsย old. the probability that a crab will be 21.7865 monthsย old. the predicted size of a crab when it is 21.7865 monthsย old. the predicted incremental increase in size for every increase in age by 21.7865ย months.arrow_forwardA researcher wishes to determine the relationship between the number of cows (in thousands) in counties in southwestern Pennsylvania and the milk production (in millions of pounds). After computing the least squares regression line, it is determined that r^2=0.9986.ย Which of the following is a correct interpretation of this value? Answer choices:ย a. About 99.86% of the changes in milk production are explained by changes in the number of cows. b. About 99.72% of the changes in milk production are explained by changes in the number of cows. c. About 99.86% of the changes in the number of cows are explained by changes in milk production. d. None of the other answers is a correct interpretation.arrow_forward
- Suppose Wesley is a marine biologist who is interested in the relationship between the age and the size of male Dungeness crabs. Wesley collects data on 1,000 crabs and uses the data to develop the following least-squares regression line whereย ?Xย is the age of the crab in months andย ?หY^ย is the predicted value ofย ?Y, the size of the male crab inย cm. ?ห=9.5603+0.3976?Y^=9.5603+0.3976X ย What is the value ofย ?หY^ย when a male crab is 24.9118 months old? Provide your answer with precision to two decimalย places. Y=arrow_forwardA recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?ฬ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. ย d. What percentage of variability in resting heart rate can be explained by variability inhours exercised?arrow_forwardSuppose 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 (ยฐF), 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 isย ?ห=โ151.05+2.65?Y^=โ151.05+2.65X. On one of the observed days, the temperature wasย 82ย ยฐF82ย ยฐFย and 68 bags of ice were sold. Determine the number of bags of ice predicted to be sold by the LSR line,ย ?หY^, when the temperature isย 82ย ยฐF.82ย ยฐF.ย Enter your answer as a whole number, rounding if necessary.arrow_forward
- Suppose there is a significant correlation between variables. describe 2ย instances in which it might be inappropriate to use the linear regression model for predictionarrow_forwardA recent study showed that the hours a person exercised in a week affected the individual'sresting heart rate. It was computed that r = -.68 and the least squares regression line was?ฬ = 83-1.4x, where x is the hours exercised and y is the resting heart rate. b. What does the value 83 tell you about the relationship between hours exercisedresting heart rate?arrow_forwardthe accompanying data represent the weights of various domestic cars and their gas mileages in the city. the linear correlation coefficient between the weight of a car and its miles per gallon in the city is r= -0.972. The least- squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is ^y =-0.0070x+44.4405ย what proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? interpret the coefficient of determination % of the variance in isย by the linear modelarrow_forward
- Select all the statements that are true of a least-squares regression line. In the equation of the least-squares regression line,ย ?ฬย y^ย is a predicted value whenย ?xย is known. The regression line is used to predictย ?yย from any value ofย ?x. The regression line maximizes the residuals between the observed values and the predicted values. The coefficient of determination,ย ?2,r2,ย measures how much of the variation in theย ?y-values is explained by the regressionย line. The slope of the regression line is resistant to outliers. The sum of the squares of the residuals is the smallest sum possible.arrow_forwardCompute the least-square regression line for predicting the president's age from the first lady's age. Round the slope and -intercept values to at least four decimal places.arrow_forwardSuppose there is a significant correlation between variables. describe 2ย cases under which it might be inappropriate to use the linear regression equation for predictionarrow_forward
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