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- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.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?For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.
- We expect poorer countries (X=1) to grow faster (Y=1) than richer countries-the table below displays countries' relative incomes and growth rates. Poorer than average (X=1) Richer than average (X=0) Ten-year growth above Ten-year growth below average (Y=1) average (Y=0) 0.38 0.14 0.13 a) Find the covariance between the two variables. 0.35 b) Interpret in plain words the independence between X and Y. (up to 40 words)Consider the AR(2) process Xt = 0.7 Xt-1-0.1 Xt-2 + Zt,A correlation of r=0.85 is found between weekly sales of firewood and cough drops over a 1-year period. Which of the following is true? (a) There is a pretty strong positive linear relationship between sales of firewood and cough drops. (b) Fire must be the cause of coughing. (c) Temperature is a possible lurking variable that is behind this relationship. (d) Both (a) and (c) are true. (e) None of the above.
- One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks: 81 Percent return, X New adults, Y 74 6 66 52 73 62 52 12 15 16 45 17 62 18 46 18 11 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line for predicting y from x using the information below: n=10 >x, = 613 , Ex = 38959, Ey; = 126, Ey = 1808, Ex,y; = 7333 (Show the details of your work.) X denotes the percent of adult sparrowhawks that return to a colony from the previous year, and Y denotes the number of new adult birds that join the colony.2 Assume you fit a logistic regression for binary Y [i.e., replace EY in linear regression by log(EY/(1-EY))=log(odds)]. Instructor claims: beta for the main effect is log(OR), and beta for interaction effect is log(ROR), where ROR denotes the ratio of the odds ratio. Explain your agreement or disagreement.Consider an MA(2) model: STEPS -Write the equation of the M(2) model-Determine the model based on the delay operator.- Find the expected value of the model- Find the variance of the model.- Find the covariances associated with 1,2, and s steps.- Find the associated correlation indices of 1,2, and s steps.- Assume that information is available up to time $h$ and the function that contains the accumulated information f(h, h-1,……), determine the forecasts and the error associated with 1,2, and s steps.