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Q13 14
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- 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?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?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?
- Sales of a video game released in the year 2000 took off at first, but then steadily slowed as time moved on. Table 4 shows the number of games sold, in thousands, from the years 20002010. a. Let x represent time in years starting with x=1 for the year 2000. Let y represent the number of games sold in thousands. Use logarithmic regression to fit a model to these data. b. If games continue to sell at this rate, how many games will sell in 2015? Round to the nearest thousand.Does a linear, exponential, or logarithmic model best fit the data in Table 2? Find the model.What situations are best modeled by a logistic equation? Give an example, and state a case for why the example is a good fit.
- World Population The following table shows world population N, in billions, in the given year. Year 1950 1960 1970 1980 1990 2000 2010 N 2.56 3.04 3.71 4.45 5.29 6.09 6.85 a. Use regression to find a logistic model for world population. b. What r value do these data yield for humans on planet Earth? c. According to the logistic model using these data, what is the carrying capacity of planet Earth for humans? d. According to this model, when will world population reach 90 of carrying capacity? Round to the nearest year. Note: This represents a rather naive analysis of world population.Suppose we fit a regression line to predict the number of incidents of skin cancer per 1,000 people from the number of sunny days in a year. For a particular year, we predict the incidence of skin cancer to be 1.5 per 1,000 people, and the residual for this year is 0.5. Did we over or under estimate the incidence of skin cancer? Explain your reasoning.What does this data mean if the values are logistic regression analysis of presence of sarcopenia as the dependent variable OR (95% CI) p-value 3.069 (1.42-6.62) 0.004
- 28. When would a survival analysis model be used instead of a logistic regression model?a) Give a practical interpretation of the y-intercept of the regression line. b) What is the best-predicted value for the median hourly wage gain for the fifteenth year of schooling? c) The actual wage gain for the fifteenth year of schooling was 14%. How close was the predicted wage gain present to the actual value, i.e. what is the residual?A safety engineer uses simple logistic regression tostudy the relationship between occupancy years (x)and evacuation decision (y), under a majorhurricane forecast. Each occupant willevacuate (Y = 1) or stay (Y = 0). Sample dataprovides the estimated logit function:w = 2.83 − 0.24x. Estimate the odds that ahomeowner of 10 years will evacuate.