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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 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?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 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.The table below shows the results of an experiment involving the growth of bacteria. Write a power regression equation for this set of data, rounding all values to three decimal places. Using this equation, predict the following… The bacteria’s growth, to the nearest integer, after 15 minutes. The amount of time, to the nearest minute, for there to be 4,000 bacteria present.A social science professor wants to determine if the amount of time that a student, who is in a relationship, spends with his or her partner is related to that same student’s academic performance. A random sample of students who are in a relationship has been taken, and the table below shows the amount of time (in hours) spent by each sample on his or her partner in a week, as well as the average grade (with 75.00 as the passing mark). a. Find the regression equation and construct the scatter plot diagram.b. Predict the grade of a student who spends 118.72 hours per week on his or her partner.c. Calculate the total variation.d. Compute the standard deviation of the estimate.
- 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?Using the previous regression model, what salary would you expect a 23 year old male student with a 3.5 GPA to expect? Round your answer to 1 decimal and express in $1,000's (same format the Salary variable has in the Excel dataset, so $50,000 would be 50.0).wrie down the estimated regression equation?
- The following data came from 6 people randomly selected from a population of children between the ages of 10 and 17. It shows their age and the number of push-ups they can do. Based on the linear regression equation, what expectation, on average, would we have for the number of push-ups 15-year olds can do? Round to the nearest whole number.Suppose that a simple linear regression model is appropriate for describing the relationship between y = house price and x = house size (sq ft) for houses in a large city. The true regression line is y = 23,000 + 48x and ? = 4000. (a) What is the average change in price associated with one extra sq ft of space?$ With an additional 100 sq ft of space?$ (b) What proportion of 1800 sq ft homes would be priced over $110,000? (Round your answer to four decimal places.)Under $100,000? (Round your answer to four decimal places.)Imagine a regression line that relates y = average systolic blood pressure to x = age. The average blood pressure for people 40 years old is 90, while for those 55 years old the average is 130. What is the estimated average systolic blood pressure for people who are 50 years old? (Round the answer to the nearest whole number.)