1. The relationship between energy consumption and householdincome was studied, yielding the following data on householdincome X (in units of $1000/year) and energy consumption Y(inunits of 10^8 Btu/year).EnergyHousehold income (x)consumption (y)20.01.83.030.54.840.055.160.374.988.495.2a. Estimate the linear regression equation.5.06.57.09.09.1b. If x=50 (household income of $50,000), estimate the averageenergy consumed for households of this income. What wouldyour estimate be for a single household?

The independent variable is Household income. The dependent variable is Energy consumption. We have…

Answered: 1. The relationship between energy…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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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?
Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
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?
Can the average rate of change of a function be constant?
Just as you are about to estimate a regression, massive sunspots cause magnetic interference that ruin all electrically powered machines (e.g., computers). Instead of giving up and flunking, you decided to calculate estimates from your data (on per capita income in thousands of U.S. dollars as a function of the percent of labor force in agriculture in 10 developed countries) manually. Your data are given below. Country % in Agriculture Per Capita Income A 9 6 B 10 8 C 8 8 D 7 7 E 10 7 F 4 12 G 5 9 H 5 8 I 6 9 J 7 10 Do a scatter plot between % in Agriculture and Per Capita Income using Excel. Place % in Agriculture on the X-axis. Copy and paste the scatter plot in the space below. Comment on the nature of the relationship between % in Agriculture and Per Capita income. Note: Use the numbers in the data as given. Do not convert those to percentage. Use Excel to compute Covariance and…
45. Table 1.2 shows the mean annual compensation of construction workers. bab Abor Cesaione TABLE 1.2 Construction Workers' Average Annual Compensation Annual Total Compensation (dollars) Year 1999 42,598 2000 44,764 2001 47,822 2002 48,966 Source: U.S. Bureau of the Census, Statistical Abstract of the United States, 2004-2005. (a) Find the linear regression equation for the data. (b) Find the slope of the regression line. What does the slope represent? (c) Superimpose the graph of the linear regression equation on a scatter plot of the data. (d) Use the regression equation to predict the construction workers' average annual compensation in the year 2008. Tabl
(a) Run linear regression on the closing price data for BTC in the range of 12/15/2020 to12/28/2020. Report the r-squared value on your training data. Use this to predict BTCclosing prices on 1/1/2021 and 1/8/2021. How close are your predictions to the actual?Repeat with polynomial regression.(b) Run linear regression on the closing price data for BTC in the range of 2/2/2021 to 2/15/2021.Report the r-squared value on your training data. Use this to predict BTC closing priceson 2/19/2021 and 2/21/2021. How close are your predictions to the actual? Repeat withpolynomial regression.(c) What is the daily rate of change on average of BTC closing prices based on your predictionsobtained from regression on the data in the range of 12/15/2020 to 12/28/2020. What aboutfor 2/2/2021 to 2/15/2021?
The data in Table 1 reports the aggregate consumption (Y, in billions) and disposable income (X, in billions) for the prosperous land of Kumandra. Draw a scatter diagram for the data and determine by inspection if there exists an approximate linear relationship between Y and X. Approximately draw a straight-line between the plotted values. Can we use this data for a linear regression model? Why?
1. (30 pts) We wish to determine a regression equation that relates the length of an infant (in cm) to age (in days), gender and weight at birth (in kg). Below is portion of the regression analysis derived using a software. *Note: under the gender variable: male and female categories are assigned a value of 1 and 0, respectively. Std. Err. 0.0980 Source Coef. Model Residual 316.8866 age weight gender intercept 0.4798 0.4020 1.3113 71.4734 8 1.0454 1.9591 19.53 7.7829 a. What is the sample size for this problem? b. Write the estimated regression equation, interpret each slope coefficients, use the proper unit of measurement. c. Test for significance of the Bage, Bweight, and Bgender at the 99% confidence level. d. From (b) which parameter/s is/are statistically significant. e. Test whether or not there is a significant relationship between the infant's length and the independent variables. Use a .01 level of significance. Use only the critical value approach. f. Provide the Coefficient…
Consider the following estimated regression model relating annual salary to years of education and work experience. Estimated Salary = 11,507.30 + 3258.45 (Education) +811.24(Experience) Suppose an employee with 10 years of education has been with the company for 12 years (note that education years are the number of years after 8th grade). According to this model, what is his estimated annual salary? Tables Keypad

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