2. Derive an approximate expression for the MSE of the ratio estimator ŷURatio and discuss under what condition will this estimator be more precise as compared to the estimator U,SRS.
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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.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?Can the average rate of change of a function be constant?
- The coefficients of variation for each data set are A, More than 5 percentage point apart B, Within 5 percentage points of each other Therefore, the systolic measurements vary A, Significantly less than B, Significantly more than c, about the same asGive an example of a variable that can be used asinstrumentfor the following endogeneity problems. In eachcase,explain why you think this is a good instrument.i.Y = Demand for Ethanol& X =EthanolPriceii.Y = Earnings & X = Leisure TimeThe variation of Y around its mean can be decomposed into which two parts?
- In addition, provide the (estimated) standard error of the estimator that you use in 1a.State the conditions in which the separate and combined ratio estimate methods are used instead of the simple ratio estimator ? (Answer should be correct with all the conditions)Identify the estimates and estimators from the model (p1). What is thedifference between estimates and estimators?
- Q1 (а) і. 10,000 vehicle speed traffic data were collected during the weekday on route FT050 at Batu Pahat, Johor. Suggest how to quantify and describe the basic characteristic of this data. Then explain how the method you suggested can help others to understand the data.The deviation of each observation (x) from the mean of the predictor variable is positive for every point in what quadrants? * Y (2) 1) 3 4)For SRSWOR (N,n), find the ratio estimator of population mean. Show that the estimator is biased.
