Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.3, Problem 3AYU
To determine
To find: The mean and standard deviation for the least squares regression model
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consider the regression model Yi = β0 + β1Xi +ui. suppose you know that β0 = 0. derive a formula for the least square estimator of β1
The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962.
Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree.
The least-squares regression equation is y=784.6x+12,431 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7962.
In a particular region, 26.5 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $29,889. Is this income higher or lower than what you would expect? Why?
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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- Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardConsider a simple linear regression model Yi = Bo + B1xi + Ei, i= 1,2, 3 with x; = i/3 for i = 1, 2, 3. Assume that %3| E1 1 -1 0 E = E2 ~ N -1 E3. 3 What is the smallest variance for an unbiased estimate of B1?arrow_forwardConsider a linear regression model Yi = ao + Bx; + €;, where ao is a constant and €¡, i = 1, 2, ., n, is a random error. Derive an expression of B, the estimate of B, using the method of least squares. %3D Clearly show ALL your work including the derivative-finding and equation-solving.arrow_forward
- Find the simple regression line y=α+βx for the pairs of points belonging to the independent and dependent variables (xi,yi) , respectively. Also, interpret the result by calculating the Pearson correlation coefficient.arrow_forwardA regression was run to determine if there is a relationship between the happiness index (y) and life expectancy in years of a given country (x). The results of the regression were: ŷ=a+bx a=-0.523 b=0.177 (a) Write the equation of the Least Squares Regression line of the form j= 0.177 +| -0.523 (b) Which is a possible value for the correlation coefficient, r? O 1.936 O -0.632 O-1.936 O 0.632 (C) If a country increases its life expectancy, the happiness index will O decrease O increase (d) If the life expectancy is increased by 1 years in a certain country, how much will the happiness index change? Round to two decimal places. (e) Use the regression line to predict the happiness index of a country with a life expectancy of 64 years. Round to two decimal places.arrow_forwardThe least-squares regression equation is y=620.6x+16,624 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7004. In a particular region, 28.3 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,389. Is this income higher than what you would expect? Why?arrow_forward
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