M GmailYouTube MapsJUN 15, 1. TL. TO PITThe accompanying table shows the number of bacteria present in a certainculture over aL4 hour period, where x is the time, in hours, and y is thenumber of bacteria.Write an exponential regression equation for this set ofdata, rounding all coefficients to the nearest thousandth. Using this equation,determine how long, to the nearest tenth of an hour, until there are 13677bacteria.Hours (x) Bacteria (y)10031111913331660 S M GmailYouTube MapsHours (x) Bacteria (y)10031111913333166941774Copy Values for Calculator2]Send a chat

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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 1TI: Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use...

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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?
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?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
The accompanying table shows the number of bacteria present in a certain culture over a 4 hour period, where x is the time, in hours, and y is the number of bacteria. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the number of bacteria present after 16 hours, to the nearest whole number.
The following table shows the number, in millions, of women employed outside the home in the given year.Use regression to find a quadratic model for the data.
Suppose a psychologist used number of minutes of sleep in the night before a quiz to predict the time needed to finish the quiz using simple linear regression. The unstandardized coefficient (B in SPSS) is 5. If the psychologist converts the unit of sleep duration from minute to hour (a value of 60 [minutes] is changed to a value of 1 [hour]) and do the regression again, what is the unstandardized coefficient of sleep in this analysis using hour as the unit?
Suppose that a researcher, using wage data on 200 randomly selected male workers and 240female workers, estimates the OLS regressionW age ˆ =10(0.2)+2(0.4)× M ale, R2 = 0.10, SER = 4,where Wage is measured in dollars per hour and Male is a binary variable that is equal to 1 if theperson is a male and 0 if the person is a female. Define the wage gender gap as the difference inmean earnings between men and women.1. What is the estimated gender gap?2. Is the estimated gender gap significantly different from 0? (Compute the p-value for testingthe null hypothesis that there is no gender gap.)13. Construct a 95% confidence interval for the gender gap.4. In the sample, what is the mean wage of women? Of men?5. Another researcher uses these same data but regresses Wages on Female, a variable that isequal to 1 if the person is female and 0 if the person a male. What are the regression estimatescalculated from this regression?W age ˆ = _ + _ × F emale, R2 = _, SER = _.
Suppose a researcher collects data on houses that have been sold in a particular neighbourhood over the past year, and obtains the regressions results in the table shown below. A family purchases a 2000 square foot home and plans to make extensions totalling 500 square feet. The house currently has a pool, and a real estate agent has reported that the house is in excellent condition. However, the house does not have a view, and this will not change as a result of the extensions. According to the results in column (1), what is the expected DOLLAR increase in the price of the home due to the planned extensions?
A researcher investigates the relationship between cigarette smoking (X) and work absences (Y). The number of cigarettes smoked daily and the number of days absent from work due to illness are collected for N= 12 employees. The preliminary results are below: What is the regression equation? How many absences (Y) would expect someone who smokes X = 10 cigarettes a day to have?
The following estimated regression model was developed relating yearly income (Y in $1,000s) of 30 individuals with their age in years (X1) and their gender (X2) (0 if male and 1 if female). The yearly income of a 24-year-old female individual is
Fit a linear-regression model relating annual inci- dence of diabetes to time period. (For this purpose, score the time period as 1 if 1970−1974, 2 if 1975−1979, . . . , 5 if 1990−1994.)

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