Problem 6. tribution of the form You are provided samples of an exponential dis- { fx(x) = exp(-7), p(-), *≥0, x 0, elsewhere, where is an unknown (positive) parameter. Find the method of moments estimator for and compute its variance.
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- What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?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?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?
- 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?Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.Problem 2. Show that D₁ = (DFFITS;)² MSE (1) (p+1)MSE' where MSE() is the mean squared error after the i-th data point is omitted.
- Q. 4 The pdf of the age-of babies, x years, being brought to a clinic is given by /(x) =D 제(2-x); 03. (a). Differentiate the different types of linear regression and describe the use of regression in geographical study. (b). Calculate the value of the slope, b, for observations of n = 22, r2 = 0.73, standard deviation of x = 2.3 and the regression sum of square = 1324.Below is the Minitab display of the scatterplot and regression line for a sample of 10 pharmacies. The pharmacies are used to examine the relation between prescription sales volume and the percentage of prescription ingredients purchased directly from the supplier. Use the Minitab display to answer questions 22 through 25. Prescription Sales versus % of Prescription Ingredients Analyis y=4.70+1.97x 140 120 100 80 60 40 20 10 20 30 40 50 60 70 % of Prescription Ingredients Question 22. A student calculates the linear correlation coefficient and gets r = 1.18. Which of the following statements correctly explains how you know that student's calculation is incorrect? (a) The value obtained for r cannot be more than 1. (b) The value obtained for r cannot be positive. (c) The value obtained for r should be -1.18. (d) All of the above. Prescription SalesSuppose that n = 50, i.i.d. observations for (Yi, Xi) yield the followingregression results: Ŷ= 49.2 + 73.9X, SER = 13.4, R2 = 0.78. (23.5) (16.4)Another researcher is interested in the same regression, but makes an errorwhen entering the data into a regression program: The researcher enterseach observation twice, ending up with 100 observations (with observation1 entered twice, observation 2 entered twice and so forth).a. Using these 100 observations, what results will be produced by theregression program? (Hint: Write the “incorrect” values of the samplemeans, variances, and covariances of Y and X as functions of the “correct”values. Use these to determine the regression statistics.) Ŷ = ____ + ____X, SER = ____, R2 = ____. (____) (____)b. Which (if any) of the internal validity conditions are violated?1. In an epidemic, the probability of having S|D is 0.2 and P(D) = 0.1. P(S|D') = 0.04 and P (D') = 0.01. What is the P(D|S)? 2. The relationship between weight and age was found to have a linear relationship, with expression weight= 3.0 (age) +10. Predict the weight of a girl whose age is 20 years? 3. A. If a z score of 1.95 is equal to a p of 0.9744, what proportion is greater than1.95 B. From question A, what proportion is between the mean and 1.95? 4. If a the constant for a regression is 0.8 and the standard deviation for the x variables is 4 while the standard deviation for the y variables is 6. What is the correlation coefficient r? 5. In a class of 20 students, twelve take mathematics and genetics, while eight take genetics only. What is the probability of selecting a student who takes only mathematics?Suppose that a researcher wishes to test for calendar (seasonal) effects using a dummy variables approach. Which af the following regressions could be used to examine this? A regression containing intercept dummies A regression containing slope dummies A regression containing intercept and slope dummies Aregression containing a dummy varlable taking the value 1 for one observation and zero for all others 40. (0, (), and (iv) Ke and () only G and (Monly Kiland onlySEE MORE QUESTIONS