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.

Answered: Image /qna-images/answer/8579b936-710b-487e-a24f-d43f0cacd574.jpg

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?
What does the y -intercept on the graph of a logistic equation correspond to for a population modeled by that equation?
Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Such that, the dependent variable is hours of training per employee, the variable sales represents annual sales, employees is the number of employees and grant variable is a dummy equals to one if the firm received a job training grant for 2010 and zero otherwise. Please, answer the following three questions: (a) Interpret the above estimations results (only the value of the OLS coefficient for each of the explanatory variables) (b) Is the variable grant individually significant to explain the dependent variable (at 1% significance level)? Explain (c) Is the model globally significant at 1% significance level? Explain
It is known that a natural law obeys the quadratic relationship y = ax-. Whatis 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 atrandom from the domain [0, 1]?
Q5 a) Demographic data from 126 countries is obtained for the year 2017. It is hypothesized that life expectancy (Y) is dependent on number of under five deaths (X2) , polio immunization coverage (D), Per capita Govt. Exp. on Health Care (X3) (in Rs crores), Per Capita GNI (in Rs crores) (X4) and Average number of years of Schooling (Xs). Polio immunization coverage =1 if yes and 0 otherwise. Following regressions were estimated: MODEL 1: = 0.903 – 0.561X2¡ + 2.008 X3i + 0.553X4¿ + 0.778 X5i + 3.638 D (0.405) se = (1.280) (0.765) (0.712) (0.491) R? = 0.787 RSS = 1339.8 MODEL 2: P, = 1.379 + 0.594 X31 + 2.139 D se = (0.406) (0.465) R? = 0.677 RSS = 1567.28 i. Is it a time series or a cross sectional data ii. Show model 2 is a restricted version of model 1 and what is the restriction? iii. Test for the statistical significance of the restriction at 5% level. iv. Construct a 95% confidence interval for true per capita government health expenditure in model II and check whether it is…
10) The following results are from a regression where the dependent variable is COST OF COLLEGE and the independent variables are TYPE OF SCHOOL which is a dummy variable = 0 for public schools and = 1 for private schools, FIRST QUARTILE SAT which is the average score of students in the top quartile of SAT’s, THIRD QUARTILE SAT which is the average score of students in the 3rd quartile, and ROOM AND BOARD which is the cost of room and board at the school. The first set of results includes all the independent variables whereas the second set of results excludes the THIRD QUARTILE SAT variable. a) Based on these two sets of data, does there appear that multicollinearity is a problem (specifically, does it appear that THIRD QUARTILE SAT is highly collinear with the other independent variables? Explain. b) Calculate the VIF for THIRD QUARTILE SAT. c) Based on the VIF, do you think that multicollinearity is a problem? Explain.
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.…
55. Explain from the data given below whether A and B are independent. positively associated or negatively associated : N=10,000, (A) = 4500, (B) = 6000, (AB) = 3150. () (A) = 150, (a) = 250, (B) = 20o, (aB) = 125. %3D %3D %3D
Flavia wanted to know if the first sample quartile (or Q1) was an unbiased estimator of the first population quartile. She started with a large population of normally distributed grades, the first quartile of which was Q = 70. She then took a random sample of 6 tests and calculated the first quartile of the sample. She replaced those exams and repeated this process a total of 50 times. Her results are summarized in the dot plot below, where each point represents the first sample quartile of a sample of 6 exams. Based on these results, does the first sample quartile appear to be a biased or unbiased estimator of the first population quartile? Track; the first population quartile is 70.
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.
2. Consider a set of data (x;, Y;), i = 1, .., n, provided in Table 3. If we believe that x; and y; has a linear relationship, we may apply simple linear regression to fit these data to a linear model. More precisely, we try to find a and B such that the straight line y = a + Bx minimizes the sum of squared errors for all the data points: min a,8 E yi – (a + Ba; i=1

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