Concept explainers
Prices of recycled materials. Prices of recycled materials (e.g., plastics, paper, and glass) are highly volatile due to the fact that supply is constant, rather than tied to demand. An exploratory study of the prices of recycled products in the United Kingdom was published in Resources, Conservation, and Recycling (Vol. 60, 2012). The researchers employed simple linear regression to model y = the monthly price of recycled colored plastic bottles as a
ŷ = − 32.35 + 4.82x, t = 16.60(for testing H0 : β1 = 0)
r = .83,r2 = .69
Use this information to conduct the first four steps of a complete simple linear
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Statistics for Business and Economics (13th Edition)
Additional Math Textbook Solutions
Probability and Statistics for Engineering and the Sciences
Elementary Statistics Using Excel (6th Edition)
Elementary Statistics (13th Edition)
Elementary Statistics: Picturing the World (6th Edition)
Fundamentals of Statistics (5th Edition)
Applied Statistics in Business and Economics
- 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_forwardWhat is regression analysis? Describe the process of performing regression analysis on a graphing utility.arrow_forwardPlease help with unanswered questions. Thank you!arrow_forward
- A group of Maternal and Child Health public health practitioners are interested in the relationship between bacterial vaginosis (BV) and a number of negative health outcomes. Suppose the research team gathers information on a group of participants, and constructs a multiple linear regression model looking at the relationship between BV and depression, controlling for maternal age. The following is a computerized output displaying the results of their analysis.Parameter Intercept Maternal Age DepressionEstimate StandardError tValue Pr>|t|0.2186206635 -.0046496845 0.19124124150.06635040 0.00221338 0.031518843.29 0.0010 -2.10 0.0360 6.07 <.0001 A) What are the dependent and independent variables in this investigation?B) Based on the information above, was the research team justified in controlling for maternal age in this population? Why or why not?C) Write out the model in symbols. Round to 3 decimal places.D) Is there a significant association between BV and depression?arrow_forwardAssume we have data demonstrating a strong linear link between the amount of fertilizer applied to certain plants and their yield. Which is the independent variable in this research question?arrow_forwardArmer Company is accumulating data to use in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested the use of linear regression to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis follow: Month Maintenance Cost Machine Hours Jan. $ 4,200 480 Feb. 3,000 320 Mar. 3,600 400 Apr. 2,820 300 May 4,350 500 June 2,960 310 July 3,030 320 Aug. 4,470 520 Sept. 4,260 490 Oct. 4,050 470 Nov. 3,300 350 Dec. 3,160 340 Sum $ 43,200 4,800 Average $ 3,600 $ 400 Average cost per hour $ 9.00 a (intercept) $ 684.65 b (coefficient) 7.2884 Standard error of the estimate 34.469 R-squared 0.99724 t-value for b 60.105…arrow_forward
- Armer Company is accumulating data to use in preparing its annual profit plan for the coming year. The cost behavior pattern of the maintenance costs must be determined. The accounting staff has suggested the use of linear regression to derive an equation for maintenance hours and costs. Data regarding the maintenance hours and costs for the last year and the results of the regression analysis follow: Month Maintenance Cost Machine Hours Jan. $ 4,200 480 Feb. 3,000 320 Mar. 3,600 400 Apr. 2,820 300 May 4,350 500 June 2,960 310 July 3,030 320 Aug. 4,470 520 Sept. 4,260 490 Oct. 4,050 470 Nov. 3,300 350 Dec. 3,160 340 Sum $ 43,200 4,800 Average $ 3,600 $ 400 Average cost per hour $ 9.00 a (intercept) $ 684.65 b (coefficient) 7.2884 Standard error of the estimate 34.469 R-squared 0.99724 t-value for b 60.105…arrow_forwardIn a study of housing demand, the county assessor develops the following regression model to estimate the market value (i.e., selling price) of residential property within his jurisdiction. The assessor suspects that important variables affecting selling price (YY, measured in thousands of dollars) are the size of a house (X1X1, measured in hundreds of square feet), the total number of rooms (X2X2), age (X3X3), and whether or not the house has an attached garage (X4X4, No=0, Yes=1No=0, Yes=1). Y=α+β1X1+β2X2+β3X3+β4X4+εY=α+β1X1+β2X2+β3X3+β4X4+ε Now suppose that the estimate of the model produces following results: a=166.048a=166.048, b1=3.459b1=3.459, b2=8.015b2=8.015, b3=−0.319b3=−0.319, b4=1.186b4=1.186, sb1=1.079sb1=1.079, sb2=5.288sb2=5.288, sb3=0.789sb3=0.789, sb4=12.252sb4=12.252, R2=0.838R2=0.838, F-statistic=12.919F-statistic=12.919, and se=13.702se=13.702. Note that the sample consists of 15 randomly selected observations. According to the estimated model, holding all…arrow_forwardA researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix. 1) a) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Explain your decision by providing its statistical basis.arrow_forward
- A researcher collected statistics on the sales amount of a product in 120 different markets and the advertising budgets used in TV, radio and newspaper media channels for each of these markets. The sales amount are expressed in 1000 units, and the budgets are expressed in 1000$. The researcher wants to create a simple linear regression model by choosing one among the TV, radio and newspaper advertising budgets to explain the amount of sales. Accordingly, answer the following question by using the data in the "Regression Data Set" document in the appendix.1) b) In your opinion, which variable should this researcher choose as an independent variable to the simple regression model? Establish the simple linear regression model using the argument of your choice and write the equation for the model. Interpret b0 and b1.1) c) Test whether there is a statistically significant and linear relationship between the independent variable and the dependent variable by establishing the relevant…arrow_forwardThe November 24, 2001, issue of The Economist published economic data for 15 industrialized nations. Included were the percent changes in gross domestic product (GDP), industrial production (IP), consumer prices (CP), and producer prices (PP) from Fall 2000 to Fall 2001, and the unemployment rate in Fall 2001 (UNEMP). An economist wants to construct a model to predict GDP from the other variables. A fit of the model GDP = , + P,IP + 0,UNEMP + f,CP + P,PP + € yields the following output: The regression equation is GDP = 1.19 + 0.17 IP + 0.18 UNEMP + 0.18 CP – 0.18 PP Predictor Coef SE Coef тР Constant 1.18957 0.42180 2.82 0.018 IP 0.17326 0.041962 4.13 0.002 UNEMP 0.17918 0.045895 3.90 0.003 CP 0.17591 0.11365 1.55 0.153 PP -0.18393 0.068808 -2.67 0.023 Predict the percent change in GDP for a country with IP = 0.5, UNEMP = 5.7, CP = 3.0, and PP = 4.1. a. b. If two countries differ in unemployment rate by 1%, by how much would you predict their percent changes in GDP to differ, other…arrow_forwardDemand for stereo headphones and MP3 players for joggers has caused Nina Industries to grow almost 50 percent over the past year. The number of joggers continues to expand, so Nina expects demand for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers from wearing them. Demand for the players for last year was as follows: MONTH January February March April May June July August September October November December Month a. Using linear regression analysis, what would you estimate demand to be for each month next year? (Do not round intermediate calculations. Round your answers to 2 decimal places.) January February March April May June July August September October DEMAND (UNITS) November December 4,220 4,320 4,020 4,420 5,020 4,720 5,320 4,920 5,420 5,720 6,320 6,020 Forecast 6,196.67 6,388.97 6,581.28 6,773.59 6,965.90 7,158.21 7,350.51 7,542.82 7,735.13 7,927.44 8,119.74 8,312.05arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning