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Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-2. In each case, find the regression equation, letting tire first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5.
25. Gas Prices One gas station not included in the table below had a listed price of $2.78 for regular gas. Find the best predicted price of premium gas at this station. Is the result close to the actual price of $2.93 for premium gas?
Regular | 2.77 | 2.77 | 2.79 | 2.81 | 2.78 | 2.86 | 2.75 | 2.77 |
Mid-Grade | 3 00 | 2.77 | 2.89 | 2.93 | 2.93 | 2.96 | 2.86 | 2.91 |
Premium | 3.07 | 3.09 | 3.00 | 3.06 | 3.03 | 3.06 | 3.02 | 3.03 |
26. Gas Prices Using the data from the preceding exercise, find the best predicted price for mid-grade gas for a station that posted $2.78 as the price of regular gas. Is the result close to the actual price of $2.84 for mid-grade gas?
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Chapter 10 Solutions
Essentials of Statistics (5th Edition)
- Regression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493. Old Faithful Using the listed duration and interval after times, find the best predicted “interval after” time for an eruption with a duration of 253 seconds. How does it compare to an actual eruption with a duration of 253 seconds and an interval after time of 83 minutes?arrow_forwardRegression and Predictions. Exercises 13–28 use the same data sets as Exercises 13–28 in Section 10-1. In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in Figure 10-5 on page 493. Manatees Use the listed boat/manatee data. In a year not included in the data below, there were 970,000 registered pleasure boats in Florida. Find the best predicted number of manatee fatalities resulting from encounters with boats. Is the result reasonably close to 79, which was the actual number of manatee fatalities?arrow_forwardSam Jones has 2 years of historical sales data for his company. He is applyingfor a business loan and must supply his projections of sales by month for thenext 2 years to the bank. a. Using the data from Table 6–12, provide a regression forecast for timeperiods 25 through 48.b. Does Sam’s sales data show a seasonal pattern?arrow_forward
- -Using the data in Table 6–11, answer the following: What is the slope? What is the intercept? Write the regression equation. Calculate a regression forecast for month 25.arrow_forwardQ. Table provided gives data on gross domestic product (GDP) for the United States for the years 1959–2005. a. Plot the GDP data in current and constant (i.e., 2000) dollars against time. b. Letting Y denote GDP and X time (measured chronologically starting with 1 for 1959, 2 for 1960, through 47 for 2005), see if the following model fits the GDP data: Yt = β1 + β2 Xt + ut Estimate this model for both current and constant-dollar GDP. c. How would you interpret β2? d. If there is a difference between β2 estimated for current-dollar GDP and that estimated for constant-dollar GDP, what explains the difference? e. From your results what can you say about the nature of inflation in the United States over the sample period?arrow_forwardApplying the Concepts and SkillsIn Exercises, we repeat the information from Exercises. For each exercise here, discuss what satisfying Assumptions 1–3 for regression inferences by the variables under consideration would mean.ExercisesApplying the Concepts and SkillsIn each of Exercises,a. find the regression equation for the data points.b. graph the regression equation and the data points.c. describe the apparent relationship between the two variables under consideration.d. interpret the slope of the regression line.e. identify the predictor and response variables.f. identify outliers and potential influential observations.g. predict the values of the response variable for the specified values of the predictor variable, and interpret your results.Tax Efficiency.Tax efficiency is a measure, ranging from 0 to 100, of how much tax due to capital gains stock or mutual funds investors pay on their investments each year; the higher the tax efficiency, the lower is the tax. In the article…arrow_forward
- section 4.1 #30 In Exercises 25–30, determine whether the association between the two variables is positive or negative. Weekly ice cream sales and weekly average temperaturearrow_forwardNational Debt The size of the total debt owed by the UnitedStates federal government continues to grow. In fact,according to the Department of the Treasury, the debt perperson living in the United States is approximately $53,000(or over $140,000 per U.S. household). The following datarepresent the U.S. debt for the years 2001–2014. Since thedebt D depends on the year y, and each input correspondsto exactly one output, the debt is a function of the year. SoD1y2 represents the debt for each year y. Source: www.treasurydirect.govDebt (billions Debt (billionsYear of dollars) Year of dollars)2001 5807 2008 10,0252002 6228 2009 11,9102003 6783 2010 13,5622004 7379 2011 14,7902005 7933 2012 16,0662006 8507 2013 16,7382007 9008 2014 17,824 (a) Plot the points 12001, 58072, 12002, 62282, and so on ina Cartesian plane.(b) Draw a line segment from the point 12001, 58072 to12006, 85072. What does the slope of this line segmentrepresent?(c) Find the average rate of change of the debt from 2002…arrow_forwardUsing the data in Table 6–11, calculate a 3-month moving average forecast for month 12.arrow_forward
- a.State the predictors available in this model.arrow_forwardInternational Visitors The number of internationalvisitors to the United States for selected years 1986–2010 is given in the table below. If you had to pick one of these models to predictthe number of international visitors in the year2020, which model would be the more reasonablechoice?arrow_forwardQ1. The table provided gives data on indexes of output per hour (X) and real compensation per hour (Y) for the business and nonfarm business sectors of the U.S. economy for 1960–2005. The base year of the indexes is 1992 = 100 and the indexes are seasonally adjusted. a. Plot Y against X for the two sectors separately. b. What is the economic theory behind the relationship between the two variables? Does the scattergram support the theory? c. Estimate the OLS regression of Y on X. Note: on the table ( 1. Output refers to real gross domestic product in the sector. 2. Wages and salaries of employees plus employers’ contributions for social insurance and private benefit plans. 3. Hourly compensation divided by the consumer price index for all urban consumers for recent quarters.) Thank you!arrow_forward
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