Problem 2. Mean Absolute Error - Adding a Data PointSuppose we have a dataset y₁ ≤ Y2 < ... < Yn and want to minimize absolute loss on it for the prediction h.As we've seen before, the corresponding empirical risk is mean absolute error,nRabs(h) =| Yi - hnSuppose that Rabs(a)=Rabs (α + 3)=a)b)M, where M is the minimum value of Rabs(h)and a is some constant. Suppose we add to the dataset a new data point yn+1 whose value is a + 1.For this new larger dataset: What is the minimum of Rabs(h)? At what value of h is this minimumachieved?Your should only involve the variables n, M, a, and constants.Let n be odd. Let ya and yɩ be two values in our dataset such that ya < yɩ and that the slopeof Rabs(h) is the same between hYa and h= y. Specifically, let d be the slope of Rabs (h) betweenYa and yb.=1=Suppose we introduce a new value q to our dataset such that q> y. In our new dataset of n + 1values, the slope of Rabs (h) is still the same between h== Ya and hYb, but it's no longer equal tod. What is the slope of Rabs (h) between h= Ya and h= y in our new dataset? Your answer shoulddepend on d, n, q, and/or one or more constants.

Part (a)1. Understanding the Problem:You have a dataset (y1≤y2≤⋯≤yn)The mean absolute error…

Answered: Problem 2. Mean Absolute Error - Adding…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section: Chapter Questions

Problem 10T: Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s...

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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?
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Suppose that @, and ô, are unbiased estimators of the parameter 0 and that V@,) = 15 and V(@2) = 4. What is the relative efficiency of the two estimators?
A researcher collected a data set for a random sample of 930 individuals living in and around London, with data collected over 1-year period. The Table below reports the OLS coefficient estimates (intercept not reported) and standard errors (in parentheses), where the dependent variable is [100xIn(well-being)]. Commuting time/60 -0.267 (0.039) -0.14 (0.040) Age Age squared/100 0.12 (0.040) Hours worked -0.0053 (0.001) log real income 0.0267 (0.009) Married or cohabiting 0.589 (0.032) Num. of children. -0.051 (0.015) Saves Degree 0.299 (0.022) -0.022 (0.035) The explanatory variables are: Commuting time = Number of minutes of commuting time per day; Age= Age in years; Hours worked = Hours worked per week; Log of real household income = 100xLn(real household income measured in £10,000s); Num. of children = Number of children under the age of 18; Save regularly = 1 if save regularly, 0 otherwise; University degree = 1 if has a University degree, 0 otherwise. Calculate the test statistics…
If N = 150, (A) = 93, (B) = 112, (C) = 80, (BC) = 20 and (Ay) = 43, find the greatest and the least possible values of (AB) so that the data may be consistent.
The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete Ho: Md = 0 Ha: Ha 0 = 0 Ho: Md < 0 Ha: Md P-value = X-ray 4.75 7.00 9.25 12.00 5 17.25 6 29.50 7 5.50 8 6.00 9 8.00 10 8.50 11 9.25 12 11.00 13 12.00 14 14.00 15 17.00 16 18.00 = 0 1 2 3 4 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = 0.534 0.000 X X State the conclusion in the problem context. We fail to reiect H.…
A coffee shop owner offers two brands of coffee, Brand "A" and Brand "B". The proportion of clients that prefer Brand "A" is 60%. Recently, the price of Brand "A" went up. The proportion of clients that buy brand "A" among the first 15 customers that enter the shop after the change in price is an estimator of the current proportion of clients that prefer Brand "A". Assume that the change in price has no effect on the preference of the clients. Then the mean squared error (MSE) of the estimator is equal to: (Give an answer of the form x.xxx, i.e. with 3 significance digits) (HINT: Carefully read the definition of MSE in Chapter 10 of the text book.)
It is known that a natural law obeys the quadratic relationship y = ax“. What is the best line of the form y = px + q that can be used to model data and minimize Mean-Squared-Error if all of the data points are drawn uniformly at random from the domain [0,1]?
The authors of a paper compared two different methods for measuring body fat percentage. One method uses ultrasound, and the other method uses X-ray technology. The table gives body fat percentages for 16 athletes using each of these methods (a subset of the data given in a graph that appeared in the paper). For purposes of this exercise, you can assume that the 16 athletes who participated in this study are representative of the population of athletes. Athlete 0 Ho: Md = Ha: Md 0 < 0 5 6 7 8 9 10 11 12 13 14 15 16 X-ray 4.75 7.00 9.25 12.00 17.25 29.50 5.50 6.00 8.00 8.50 9.25 11.00 12.00 14.00 17.00 18.00 USE SALT Ultrasound 4.75 4.00 9.00 11.75 17.00 27.75 6.50 6.75 8.75 9.75 9.50 12.00 12.25 15.75 18.00 18.50 X Find the test statistic and P-value. (Use a table or SALT. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = 0.000 Mx-ray ultrasound.)
3. You are curious to understand if there is a relationship between the average grade (in %) that students received in Assignment 1, 2, and 3 of ECOR 2050 (assignments that covered midterm material) and their grade (in %) in the Midterm of the course. You are limited to collect 7 sets of data (midterm vs average assignments). For that, you can check the google sheets to find grades of assignment 1, 2, and 3 and midterm for 7 students. You should be careful that your data set is not biased. a) Collect the information and record them in the table below (please use a typed table/numbers as we need to copy/paste your numbers into Excel for checking your solution and marking). Mention how you ensured that your data set is random and unbiased. Student 2 3 4 6. 7 Grade (%) Average of Assignment 1, 2, and 3 (assignments before midterm) Midterm b) Using the collected information, conduct a simple linear regression analysis and find the regression line. Also, estimate the coefficient of…

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