Determine (a) the score function s, (b) the Fisher information I. 1
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![(1) Recall that the probability mass function f for Poisson random variable X is given by
be a
9
ƒ (k) = P [X = k] = e-for k = 0, 1, 2, ..., where A is the parameter. Let x₁, ... XJ
sequence of J independent samples of X. Denote the log likelihood function by l, namely,
J
l(X|x₁,...,xj)
Determine
(a) the score function s,
(b) the Fisher information I.
=
j=1
In P [X = x₂] .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9ff5cc5-ffa0-4d62-80cc-4b5d73842eb0%2F2eab7f5f-cbf2-4143-a93e-a940edac7fa3%2F2280f0r_processed.jpeg&w=3840&q=75)
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- Consider the following data set: (x, y) : (1.0, 5.1), (1.25, 5.79), (1.5, 6.53), (1.75, 7.45), (2.0, 8.46) If the least squares approximation of the form beax is y=(3.07) e0.5056)x then the total error is: Select one: O a. 0.150 O b. 0.0015 O c. 1.150 O d. 0.015How do we do in excelThis dataset continues our saga of modeling the price of this popular Honda automobile. The dataset has now been cleaned to remove the columns with the dealership where the car was offered for sale and specific trim. (a) write out your model in econometric notation. Be very precise! (b) using the 93 observations in the dataset, estimate a model where price is a function of age, mileage and trim of the car. Be sure to avoid the dummy variable trap!! Fully report the results of your model. In this case, interpretation of the coefficients on the dummy variables is particularly important. (c) test the hypothesis that the specific trim does not affect the price of a Civic. Be sure to do all parts of the hypothesis test. (please fully describe steps if you are using Excel) Price Years Old KM EX EXT SE Sport Touring 6555 9 290363 0 0 0 0 0 9999 9 142258 0 0 0 0 0 10281 6 132644 0 0 0 0 0 12480 5 167125 0 0 0 0 0 12991 7 57398 0 0 0 0 0 12991 6 93046 0 0 0 0 0 12991…
- The accompanying data are x = cost (cents per serving) and y = fiber content (grams per serving) for 18 high-fiber cereals rated by a magazine. Cost per Serving Fiber per Serving Cost per Serving Fiber per Serving r = 35 46 49 62 r = 41 19 77 71 30 9.3 10 10 7 6.4 7 7 10 12 10 9.6 7 8 8 Cost per Fiber per Cup Cup 7 12 12 8 USE SALT 49 46 49 (a) Calculate the value of the correlation coefficient for this data set. (Round your answer to four decimal places.) 62 32.8 Interpret the value of the correlation coefficient. O There is a strong positive linear relationship between cost per serving and fiber per serving. O There is a weak negative linear relationship between cost per serving and fiber per serving. O There is a weak positive linear relationship between cost per serving and fiber per serving. O There is no correlation between cost per serving and fiber per serving. O There is a strong negative linear relationship between cost per serving and fiber per serving. 19 53 (b) The serving…We will fit a least-squares line y = Bo+ B1x to the data in the following table using x as the independent variable. 3 6 7 9 12 y 1 5 9 The mean values are: x=7 and y=5. Answer the following questions (select correct/closest choices). 1) Estimated value of the slope, B, is O 0.905 O 0.840 O 0.760 1.333 2) Estimated value of the intercept, Bo is O 1.333 -1.200 -0.320 O 3.200 3) The fitted y value when x=6 is O 3.816 O 4.664 4.240 3.604 4) The residual when x=6 is O 0.646 O 0.760 0.684 0.836 LOA set of data is best fit by y = a, Using linear least squares, determine the coefficient: Select one: a. None b. Ex, /n c. E,y, In d. E,x y,/2,x Previous page Next page
- A score S is used to predict whether a disease is present. If the score is greater than a threshold value, the corresponding person is classified as ill, otherwise as healthy. Here, the scores S; for 9 persons are given. Furthermore, it is known whether the persons are actually ill (Y, = 1) or not (Yi = 0). The data look as follows: S; | Y; 0.3 0 1.2 1 0.7 0.8 1 0.1 0.4 1 1.1 0 0.2 0 1.4 1 (a) Draw by hand the ROC curve for the given data. Explain your procedure and the calcu- lation methods. (b) Calculate the area under the curve (AUC) by hand. Does this value indicate a good or bad classification? (c) Calculate the partial area under the curve (PAUC) if the specificity is to be at least 0.65. How do you judge this value?In the following table, price of a used car is given in terms of the percentage of the car's original price. Want to estimate price of a used car based on its mileage and age. Find the best linear fit to minimize the 2-norm of the approximation error. Age Mileage Percent of Original Price 1 5000 90 2 10000 85 2 15000 80 3 15000 75 34 20000 75 20000 70 4 30000 65 55 30000 60 40000 50"ple: Find the linear least squares approximation to the data: - 1 0.5 Yi 2 4
- Braking Reaction Times: Histogram Listed below are sorted braking reaction times (in 1/10,000 sec) for male and female subjects (based on data from the RT-2S Brake Reaction Time Tester). Construct a histogram for the reaction times of males. Use a class width of 8 and use 28 as the lower limit of the first class. For the horizontal axis, use class midpoint values. Does it appear that the data are from a population with a normal distribution?HW22: Please help me answer all sections5) Using the method of Least Squares, determine the value of y when x = 3.0 in the equation y = Ae By using the given data: X 2.07 8.60 14.42 15.80 y 2 13 4
