The electric power consumed each month by a chemical plant is thought to be related to the average ambienttemperature x1, the number of days in the month x2, the average product purity X3, and the tons of productproduced X4. The past year's historical data are available and are presented in the following table....24023629027424253145919088879194100952111088949924606572252526301316300296267276252524252523878688919089979611010580847560288261503810098(a) Fit a multiple linear regression model using the above data set(b) Predict power consumption for a month in which x1 = 75°F, X2 = 24 days, X3 = 90%, and X4 = 98 tons.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section: Chapter Questions

Problem 4SGR

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What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
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?
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?2300
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?
Demand for Candy Bars In this problem you will determine a linear demand equation that describes the demand for candy bars in your class. Survey your classmates to determine what price they would be willing to pay for a candy bar. Your survey form might look like the sample to the left. a Make a table of the number of respondents who answered yes at each price level. b Make a scatter plot of your data. c Find and graph the regression line y=mp+b, which gives the number of respondents y who would buy a candy bar if the price were p cents. This is the demand equation. Why is the slope m negative? d What is the p-intercept of the demand equation? What does this intercept tell you about pricing candy bars? Would you buy a candy bar from the vending machine in the hallway if the price is as indicated. Price Yes or No 50 75 1.00 1.25 1.50 1.75 2.00
Cable 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?
According to human capital theory, a person’s earning is linked to her level of education – there is a relationship between workers income and years of education. Using data from the Labour Force Survey, a researcher found the following regression results for earnings on intercept, years of education, experience, and experience squared: Earnings = 5.24 + 0.035 educ + 0.165 exper – 0.003 exper2 (2.45) (0.012) (0.031) (0.001) Construct a 95% confidence interval for the effect of years of education on earnings ? 2. Consider an individual with 8 years of experience. What would you expect to be the return to two (2) additional years of experience (the effect on earnings)? 3. According to economic theory,…
Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply. Select all that apply: The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year The number of cars produced as a function of the number of days since the end of the last strike. The total shipping orders that are backlogged as a function of the number of ships in drydock. The number of backorders as a function of the number of assembly workers in a manufacturing company that makes the product.
Which of the following situations would have data sets or plots that could have a regression line with a positive slope? Select all that apply. Select all that apply: The cumulative number of ships launched by ship builders as a function of the number of months since the start of the year The number of cars produced as a function of the number of days since the end of the last strike. The total shipping orders that are backlogged as a function of the number of ships docked. The number of backorders as a function of the number of assembly workers in a manufacturing company that makes the product.
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. $ 5,050 820 Feb. 3,850 660 Mar. 4,450 740 Apr. 3,670 640 May 5,200 840 June 3,810 650 July 3,880 660 Aug. 5,320 940 Sept. 5,110 830 Oct. 4,900 810 Nov. 4,150 690 Dec. 4,010 680 Sum $ 53,400 8,960 Average $ 4,450 $ 747 Average cost per hour $ 6.00 a (intercept) $ 194.33 b (coefficient) 6.2201 Standard error of the estimate 144.247 R-squared 0.9517 t-value for b 14.030…
The 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. The current minimum wage is $5.15. If an employee earns the minimum wage, how many complaints can that employee expect to receive? Is the regression coefficient statistically significant? How can you tell?
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…

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