Concept explainers
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated.
Traffic in the Lincoln Tunnel Characteristics of traffic flow include density
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a.Make an approximate exponential model of
b.Express, using functional notation, the density of traffic flow when the average speed is
c.If average speed increases by
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Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
- XYZ Corporation Stock Prices The following table shows the average stock price, in dollars, of XYZ Corporation in the given month. Month Stock price January 2011 43.71 February 2011 44.22 March 2011 44.44 April 2011 45.17 May 2011 45.97 a. Find the equation of the regression line. Round the regression coefficients to three decimal places. 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 the stock price to be in January 2012? January 2013?arrow_forwardFor the following exercises, consider the data in Table 5, which shows the percent of unemployed in a city ofpeople25 years or older who are college graduates is given below, by year. 41. Based on the set of data given in Table 7, calculatethe regression line using a calculator or othertechnology tool, and determine the correlationcoefficient to three decimal places.arrow_forwardFor the following exercises, consider the data in Table 5, which shows the percent of unemployed ina city of people 25 years or older who are college graduates is given below, by year. 40. Based on the set of data given in Table 6, calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.arrow_forward
- A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel, t years since 1990, One analysis involving additional data used a cubic equation to model this data. t Years since 1990 0 2 5 7 10 12 15 17 20 21 P Price, dollars per barrel 18.91 16.22 16.63 18.20 27.04 23.47 49.63 69.04 77.46 106.92 a. Use cubic regression to model these data. Round the regression parameters to four decimal places. b. Plot the data along with the cubic model. c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020. d. What estimate does the model give for oil prices in 2015? e. The actual price of oil in December of 2015 was about 35 per barrel. What basic principle in the use of models would be violated in relying on the estimate in part d?arrow_forwardWhat does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?arrow_forwardCable TV The following table shows the number C. in millions, of basic subscribers to cable TV in the indicated year These data are from the Statistical Abstract of the United States. Year 1975 1980 1985 1990 1995 2000 C 9.8 17.5 35.4 50.5 60.6 60.6 a. Use regression to find a logistic model for these data. b. By what annual percentage would you expect the number of cable subscribers to grow in the absence of limiting factors? c. The estimated number of subscribers in 2005 was 65.3million. What light does this shed on the model you found in part a?arrow_forward
- 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_forwardThe U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. Table 7: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .854a .730 .695 6.6235 a. Predictors: (Constant), Hourly Wage Table 8: ANOVA ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1918.458 1 1918.458 129.783 .000a Residual 709.567 48 14.782 Total 2628.025 49 a. Predictors: (Constant), Hourly Wage b. Dependent Variable: Number of Complaints Table 9: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t…arrow_forwardThe U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. To facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The analyst ran a simple linear regression in SPSS. The results are shown below. Table 7: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .854a .730 .695 6.6235 a. Predictors: (Constant), Hourly Wage Table 8: ANOVA ANOVAb Model Sum of Squares df Mean Square F Sig. 1 Regression 1918.458 1 1918.458 129.783 .000a Residual 709.567 48 14.782 Total 2628.025 49 a. Predictors: (Constant), Hourly Wage b. Dependent Variable: Number of Complaints Table 9: Coefficients Coefficientsa Model Unstandardized Coefficients Standardized Coefficients t…arrow_forward
- thumbs up if correct!arrow_forwardA and T=arrow_forwardBluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is Price = B + OBedroom + yHouse Size + ALot Size Coef SE Coef Predictor T Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 0.164 Lot Size -4.36 17.02 -0.26 0.798 R-Sq=56.0% R-Sq (adj)=54.6% S= 25023 Source DF MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. b) Fill in the missing values *, **, c) Use the p-value approach to determine if ø is significant at the 5% significance level and d) Is y significantly different from -0.5? e) Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. f) Give an interpretation to the term "R-sq" and comment…arrow_forward
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