(a) Say you are given two datapoints (7,31) = (2,7) and (x2, 32) = (3,11). You...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(a) Say you are given two datapoints (7,31) = (2,7) and (x2, 32) = (3,11). You wish to fit a polynomial model to this dataset. What is the optimal degree 0 polynomial fit to this data? Show all work. Hint: what is w for a degree 0 model? (b) In the previous question, which degree would cause the cost function to be zero? Provide this model (i.e. compute the weight vector) using any method you like.. (c) For simple linear regression (i.e. p= 1), what does w represent? How does our estimate of w change as the variance of X increases? To illustrate your answer above, draw two datasets (scatter plots) on the axes below: one where the variance of X is low and one where it is high. Sketch the line of best fit for each. Var(X): low YA Var(X): high (d) Say I have a dataset with p= 3. After using the analytic solution for linear regression I come up with this linear model: hu(x)= 72 +0.01z - 15.6x2 - 7.5x3 Assuming the features are roughly on the same scale, which feature is the most important for predicting the outcome? Which feature is least relevant to the outcome? (e) The graph below shows an elbow plot for a series of polynomial models, with degree on the x-axis and RSS for a training dataset on the y-axis. Which polynomial model would you choose as the "best" model and why? RSS 0 1 4 5 6 7 polynomial degree 8 9 10 (f) Building on the previous question, say you were given a test dataset, and computed predic- tions for this test dataset using each polynomial model (deg 0-10). Sketch roughly what you would expect the RSS for this test dataset to look like (on the axes above). Hint: which degree would cause the minimum test error? (a) Say you are given two datapoints (7,31) = (2,7) and (x2, 32) = (3,11). You wish to fit a polynomial model to this dataset. What is the optimal degree 0 polynomial fit to this data? Show all work. Hint: what is w for a degree 0 model? (b) In the previous question, which degree would cause the cost function to be zero? Provide this model (i.e. compute the weight vector) using any method you like.. (c) For simple linear regression (i.e. p= 1), what does w represent? How does our estimate of w change as the variance of X increases? To illustrate your answer above, draw two datasets (scatter plots) on the axes below: one where the variance of X is low and one where it is high. Sketch the line of best fit for each. Var(X): low YA Var(X): high (d) Say I have a dataset with p= 3. After using the analytic solution for linear regression I come up with this linear model: hu(x)= 72 +0.01z - 15.6x2 - 7.5x3 Assuming the features are roughly on the same scale, which feature is the most important for predicting the outcome? Which feature is least relevant to the outcome? (e) The graph below shows an elbow plot for a series of polynomial models, with degree on the x-axis and RSS for a training dataset on the y-axis. Which polynomial model would you choose as the "best" model and why? RSS 0 1 4 5 6 7 polynomial degree 8 9 10 (f) Building on the previous question, say you were given a test dataset, and computed predic- tions for this test dataset using each polynomial model (deg 0-10). Sketch roughly what you would expect the RSS for this test dataset to look like (on the axes above). Hint: which degree would cause the minimum test error?
Expert Answer:
Related Book For
Posted Date:
Students also viewed these programming questions
-
a. Prepare a plot of the CPI data. Based on this plot, which of the time series forecasting techniques covered in this chapter would not be appropriate for forecasting this time series? b. Apply...
-
What relationship would you expect to find between the level of development of a countrys financial system and its level of economic development? Explain in terms of the countrys level of savings and...
-
According to the National Sleep Foundation, children between the ages of 6 and 11 years should get 10 hours of sleep each night. In a survey of 56 parents of 6 to 11 year olds, it was found that the...
-
Why dont all firms use bootstrap financing? Are there any dangers with this approach? What are the benefits of having some financial slack (e.g., some extra cash in reserve)? What are the costs of...
-
Reconsider the data from Problem 56. What is the capital recovery cost of Model 127B? Data from problem 56 Octavia Bakery is planning to purchase one of two ovens. The expected cash flows for each...
-
Ferraro, Inc. established a stock-appreciation rights (SAR) program on January 1, 2010, which entitles executives to receive cash at the date of exercise for the difference between the market price...
-
Q1. A common base transistor amplifier has an input resistance of 20 Q and output resistance of 100 kn. The collector load is 1 kQ. If a signal of 500 mV is applied between emitter and base, find the...
-
Hemoglobin absorbs light of wavelength 585nm, which means that lasers of that wavelength are often used to remove blood-induced blemishes such as birthmarks. Using the specific heat and heat of...
-
Total demand ( D ) is 3 5 0 units, the holding cost per unit ( Ch ) is equal to ( 0 . 6 ) and the ordering cost per order ( Co ) is ( 1 1 . 5 ) . Calculate the total costs for each plan and state...
-
If a company wants to maximize their profit when they sell their inventory, which of the following managerial accounting decisions would help them achie desired goal? O The management team should...
-
How do power dynamics and hegemonic ideologies perpetuate systemic inequalities, and what strategies can be employed to challenge and dismantle oppressive structures in pursuit of social justice and...
-
Consider a multi-factor key rate model with key rates being YTM on 2, 5, 10, and 30-year par ponds. In lectures, we have shown that the price p(x) of a T-year par dp. 100 bond, where y is the bond's...
-
How does society conceptualize and delineate the notion of deviance, and what multifaceted factors could potentially precipitate individuals to engage in behavior classified as "deviant"?
-
Well-Bread Grain Company is a price-taker and uses target pricing. The company has just done an analysis of its revenues, costs, and desired profits and has calculated its target full product cost....
-
In Exercises 1-2, rewrite each verbal statement as an equation. Then decide whether the statement is true or false. Justify your answer. 1. The logarithm of the difference of two numbers is equal to...
-
Define chase strategy.
-
As the Cottrell Bicycle Co. of St. Louis completes plans for its new assembly line, it identifies 25 different tasks in the production process. VP of Operations Jonathan Cottrell now faces the job of...
-
Chung Manufacturing is considering the introduction of a family of new products. Long-term demand for the product group is somewhat predictable, so the manufacturer must be concerned with the risk of...
-
Based on the photographs in Figure 26.13, in which segment(s) is the Antp gene normally expressed? Figure 26.13: (a) Normal fly (b) Antennapedia mutant
-
The bush baby, a small African mammal, is a remarkable jumper. Although only about 8 inches long, it can jump, from a standing start, straight up to a height of over 7 feet! Use the particle model to...
-
Hicham El Guerrouj of Morocco holds the world record in the 1500 m running race. He ran the final 400 m in a time of 51.9 s. What was his average speed in mph over the last 400 m? A. 14.2 mph B. 15.5...
Study smarter with the SolutionInn App