Over 25 years you collect data on:Year end percent change in stock price of ABCInc. (Y)Year end percent change in S&P 500. (X)Regression findingY = 0.12 + 1.4(X); sɛ= 0.7Intrepretation-For any given value of X, wewould expect 95% of all scores of Y to fallwithin ±1.96 * 0.7 points of the predictedvalue. Is this a high or low risk?

Linear regression is the model which assesses the relationship between a dependent and an…

Over 25 years you collect data on: Year end percent change in stock price of ABC Inc. (Y) Year end percent change in S&P 500. (X) Regression findingY = Ö.12 + 1.4(X) ; sɛ= 0.7 Intrepretation-For any given value of X, we would expect 95% of all scores of Y to fall within ±1.96 * 0.7 points of the predicted value. Is this a high or low risk?

Over 25 years you collect data on: Year end percent change in stock price of ABC Inc. (Y) Year end percent change in S&P 500. (X) Regression findingY = Ö.12 + 1.4(X) ; sɛ= 0.7 Intrepretation-For any given value of X, we would expect 95% of all scores of Y to fall within ±1.96 * 0.7 points of the predicted value. Is this a high or low risk?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.1: Logistic Functions

Problem 16E: Cable TV The following table shows the number C. in millions, of basic subscribers to cable TV in...

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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?
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?
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?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Special Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. Fluorescent Bulbs Compact fluorescent light bulbs save energy when compared with traditional incandescent bulbs. Our green energy campaign includes efforts to get local residents to exchange their incandescent bulbs fur fluorescent bulbs. Initially 200 households make the change. Market studies suggest that, in the absence of limiting factors, we could increase that number by 25 each month. In our target area, there are 250,000 households, which we take as the limiting value. Make a logistic model that gives the number of households converting to fluorescent bulbs after t months.
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. First Down The following table shows the probability P, as a percentage, of a college football team converting on fourth down when not goal to go versus the distance D, in yards, to the first down maker. 28 D = distance, in yards P = probability 1 70 2 60 3 53 4 46 5 41 6 37 7 34 8 32 a.Use exponential regression to model the data. b.Plot the data along with the exponential model. c.What probability does the model give of gaining a first down for fourth down and 10yards to go? Note: the actual probability is 28.
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?
The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.
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.
Special Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. An Epidemic In a city of half a million, there are initially 800 cases of a particularly virulent strain of flu. The Centers for Disease Control and Prevention in Atlanta claims that the cumulative number of infections with this flu strain will increase by 40 per week if there are no limiting factors. Make a logistic model of the potential cumulative number of cases of flu as a function of weeks from initial outbreak, and determine how long it will be before 100, 000 people are infected.
Special Rounding Instructions When you perform logistic regression, round the r value to three decimal places and the other parameters to two decimal places. Round all answers to two decimal places unless other-wise indicated. Magazine Sales Our new magazine initially sells 300 copies per month. Research indicates that a vigorous advertising campaign could increase sales by 20 each month if our market were unlimited. But research also indicates that magazine sales in our area are unlikely to exceed 1200 per month. Make a logistic model of projected magazine sales.
Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Design Patents The following table shows the number P of design patents awarded by the U.S. Patents and Trademark Office from 1950 through 2010. t = years since 1950 P = patents 0 4718 10 2543 20 3214 30 3949 40 8024 50 17,413 60 22,799 a.Use exponential regression to model P as a function of t. b.Plot the data along with the regression equation. c.In what years were there more patents awarded than might be expected from the model?