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- 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?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.
- 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?A researcher is attempting to explore the relationship between study duration per day (0 - 8) and the passing of the science course (Pass=1, Fail=0). For this purpose, a sample of 36 students from Alabama University are chosen. Summary of the logistic regression model has been included. Please help me understand and choose from the following below, which is the correct representation of the related logistic regression model in the summary photo attached. - PASS = 0.57 + 3.69 X SDURATION - PASS= 3.69 +0.57 X SDURATION - PASS/FAIL=3.69 + 0.57 x SDURATION - P(PASS/F(FAIL)=3.69+ 0.57 X SDURATION - PASS/FAIL= 0.57 + 3.69 x SDURATION - ln{P(PASS/F(FAIL)}=0.57 + 3.69 X SDURATION - ln{P(PASS/F(FAIL)}= 3.69+ 0.57 X SDURATIONTRUE or False 1)Logistic regression cannot be employed when the dependent variable is binary. 2)In the average linkage clustering, the distance between two clusters is defined as the average of distances between all pairs of objects, where each pair is made up of one object from each group. 3)As Monte Carlo simulation is essentially statistical sampling, the larger the number of trials used, the more precise is the result. 4)Monte Carlo simulation is an inappropriate tool to analyze cash budgets because of the inherent uncertainty of the sales forecasts on which most cash budgets are based 5)Any solution that satisfies all constraints of a problem is called a feasible solution..
- The prices of stocks or other financial instruments are often modeled with a lognormal distribution. An investor is considering purchasing stock in one of two companies, A or B. The price of a share of stock today is $1 for both companies. For company A, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.05 and σ = 0.1. For company B, the value of the stock one year from now is modeled as lognormal with parameters μ = 0.02 and σ = 0.2. a) Find the mean of the price of one share of company A one year from now. b) Find the probability that the price of one share of company A one year from now will be greater than $1.20. c) Find the mean of the price of one share of company B one year from now. d) Find the probability that the price of one share of company B one year from now will be greater than $1.20.A jar contains 7 gold, 5 silver, 4 blue, 3 red, and 1 green marbles. Two marbles are to be randomly drawn from the jar. What is the probability a sliver marble is drawn, not returned to the jar, and then a blue marble is drawn? Given the power regression model y = 25x^1.2, which is the linear regression model after transforming to a log-log graph?Consider an island that is separated from the mainland, which contains a pool of potential colonizer species. The MacArthur-Wilson theory of biogeography† hypothesizes that some species from the mainland will migrate to the island but that increasing competition on the island will lead to species extinction. It further hypothesizes that both the rate of migration and the rate of extinction of species are exponential functions, and that an equilibrium occurs when the rate of extinction matches the rate of immigration. This equilibrium point is thought to be the point at which immigration and extinction stabilize. Suppose that, for a certain island near the mainland, the rate of immigration of new species is given by the following formula. I = 5.0 ✕ 0.93t species per year Also suppose that the rate of species extinction on the island is given by the following formula. E = 1.7 ✕ 1.1t species per year According to the MacArthur-Wilson theory, how long will be required for stabilization…
- A population of 200 bass released in a lake began growing at a rate of 100 fish/yr. A second assessment performed at a later date found that there were 400 fish and the population was growing at a rate of 160 fish/yr. (Assume logistic growth dynamics.) (a) Estimate the equilibrium population size without harvesting.Suppose a new magazine initially sells 600 copies per month. Research indicates that a vigorous advertising campaign could increase sales by 40% each month if our market were unlimited. But research also indicates that magazine sales in our area are unlikely to exceed 2400 per month. Make a logistic model of projected magazine sales. a) N = 600 / 1+3e^-0.336t b) N = 2400 / 1+3e^-0.336t c) N = 40 / 1+3e^-0.336t d) N = 2400 / 1+40e^-0.336tThe market research department of a soft drink manufacturer is investigating the effectiveness of a price discount coupon on the purchase of a two-liter beverage product. A sample of 5500 customers was given coupons for varying-price discounts between 5 and 25 cents. The response variable was the number of coupons in each price discount category redeemed after one month. The data is in the picture. a. Fit a logistic regression model to the data. Use a simple linear regression model as the structure for the linear predictor.b. Does the model deviance indicate that the logistic regression model from part a is adequate?c. Draw a graph of the data and the fitted logistic regression model.d. Expand the linear predictor to include a quadratic term. Is there any evidence that this quadratic term is required in the model?