Concept explainers
In Exercises 9-12, find the regression line associated with the given set of points. Graph the data and the best-fit line. (Round all coefficients to four decimal places.) [HINT: See Example 2.]
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Finite Mathematics
- Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300arrow_forward3.4 SKILL BUILDING EXERCISES Getting Regression Lines Only Find the equation of the regression line for the following data set. x 1 2 3 y 3 3 4arrow_forwardHOW DO YOU SEE IT? Discuss how well a linear model approximates the data shown in each scatter plot.arrow_forward
- Management proposed the following regression model to predict sales at a fast-food outlet.arrow_forwardn 2011, home prices and mortgage rates fell so far that in a number of cities the monthly cost of owning a home was less expensive than renting. The following data show the average asking rent for 10 markets and the monthly mortgage on the median priced home (including taxes and insurance) for 10 cites where the average monthly mortgage payment was less than the average asking rent (The Wall Street Journal, November 26–27, 2011). (c) Using a quadratic regression model, develop an estimated regression equation to predict the monthly mortgage on the median-priced home, given the average asking rent. If required, round your answers to three decimal places. Let x represent Rent ($). Let x2 represent Rent Squared. City Rent ($) Mortgage ($) Atlanta 840 539 Chicago 1,062 1,002 Detroit 823 626 Jacksonville 779 711 Las Vegas 796 655 Miami 1,071 977 Minneapolis 953 776 Orlando 851 695 Phoenix 762 651…arrow_forwardIn a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least‑squares regression line was ?̂ =10+0.9?, where ?y represents the final exam score and ?x is the midterm exam score. Suppose Joe scores an 80 on the midterm exam. What would be the predicted value of his score on the final exam?arrow_forward
- A well-known university is interested in how salary (in thousands of dollars) is predicted from years of service for faculty and administrative staff. Below are the estimated regression equations.Faculty (n = 170): ŷ = 60 + 1.1xAdmin. (n = 155): ŷ = 57 + 1.5x a) How much would a faculty member be earning after 5 years of service? b) In how many years will an administrator earn the same amount as in a)?arrow_forwardManagement proposed the following regression model to predict sales at a fast-food outlet. y=β0+β1X1+β2X2+β3X3+εy=β0+β1X1+β2X2+β3X3+ε where X1X1 =number of competitors within one mile X2X2 = population within one mile (1000s) X3={1ifdrive−upwindowpresent0OtherwiseX3={1ifdrive−upwindowpresent0Otherwise YY=Sales($1000s) The following estimated regression equation was developed after 20 outlets were surveyed. y=10.1−4.9x1+6.6x2+15.9x3y=10.1−4.9x1+6.6x2+15.9x3 a. What is the expected amount of sales attributable to the drive-up window? b. Predict sales for a store with two competitors, a population of 8,000 within one mile, and no drive-up window.arrow_forwardAssume that there is a positive linear correlation between the variable R (return rate in percent of financial investment) and the variable t (age in years of the investment) given by the regression equation R = 2.5t + 5.3. 1- Without further information, can we assume there is a cause-and-effect relationship between the return rate and the age of the investment? 2- If the investment continues to grow at a constant rate, what is the expected return rate when the investment is 7 years old? 3- If the investment continues to grow at a constant rate, how old is the investment when the return rate is 32.8%?arrow_forward
- Management proposed the following regression model to predict sales at a fast-food outlet. y = ?0 + ?1x1 + ?2x2 + ?3x3 + ? where x1 = number of competitors within one mile x2 = population within one mile (1,000s) x3 = 1 if drive-up window present 0 otherwise y = sales ($1,000s). The following estimated regression equation was developed after 20 outlets were surveyed. ŷ = 10.5 − 4.2x1 + 6.8x2 + 15.5x3 (a) What is the expected amount of sales (in dollars) attributable to the drive-up window? $ (b) Predict sales (in dollars) for a store with two competitors within one mile, a population of 8,000 within one mile, and no drive-up window. $ (c) Predict sales (in dollars) for a store with one competitor within one mile, a population of 3,000 within one mile, and a drive-up window. $arrow_forwardTake a look at the scatterplot below with the corresponding best-fit regression line. What is a possible “R” value for the scatterplot? -0.8 -1 0 0.8 1arrow_forward
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