(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...
-
(a) In the proof of Lemma 7.2.2 it is claimed that for some integers x, y, ax+py = 1. Based on this proof, give a different, much shorter proof of Lemma 7.2.9 that uses gcd (s, u) = 1. (b) Assume d =...
-
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...
-
A distribution we didn't discuss is the Bernoulli distribution. It is a binomial distribution with n = 1. In other words, it is the number of successes (0 or 1) in a single trial when the probability...
-
The equity sections from the 2020 and 2021 balance sheets of Fab-Form Industries Inc. appeared as follows: Fab-Form Industries Inc. Equity Section of the Balance Sheet December 31, 2020 Contributed...
-
Sampling for attributes is often used to allow an auditor to reach a conclusion concerning the rate of occurrence in a population. A common use in auditing is to test the rate of deviation from a...
-
All-Star Bat Manufacturing, Inc., supplies baseball bats to major and minor league baseball teams. After an initial order in January, demand over the six-month baseball season is approximately...
-
Blood is flowing through an artery partially clogged by cholesterol. Because of the clog, the effective diameter of the artery is small enough that the viscosity of the blood cannot be neglected. A...
-
The information below pertains to the retiree health care plan of Thompson Technologies: Thompson began funding the plan in 2024 with a contribution of $127,000 to the benefit fund at the end of the...
-
A firm has a debt-to-equity ratio of .5 and a market-to-book ratio of 2. What is the ratio of the book value of debt to the market value of equity?
-
(a2) Blue, Finland's second largest homebuilder, has approached Wilson with an offer to buy 75,000 windows during the coming year. Given the size of the order, Blue has requested a 40% volume...
-
A Planner wants to determine the required safety stock to achieve a 99.5% service level. Data for the last 12 periods is shown below Period 1 2 3 4 5 6 7 8 9 10 11 12 Demand 1250 1600 1345 1090 2100...
-
V = 1.0 m/s 20 P=0.10 Santa Claus loses his footing and slides down a snowy roof at an angle of 20, with an initial velocity (vo) of 1.0 m/s. Santa has a mass of 82 kg. Between the surfaces of the...
-
where a Consider the charge configuration shown 92-187 nC, q3= 113 nC, and q = -172 nC. a) What is the force exerted by 92 on 91? F. i + 9291 = b) What is the force exerted by 94 on 91? F + 9491 = c)...
-
Nampower treats high income earners in Kleine Kuppe as one market and low-income earners in Katutura as another market. The marginal revenue function of an additional Kilowatt of electricity from the...
-
You bought an $8,000 car last year with a $1,000 down payment and a $7,000 loan. The car now has a market value of $6,000 and the loan balance is currently $5,500. Related to the car purchase Select...
-
How will relating product contribution margin s to the amount of the constrained resource they consume help a company maximize its profits?
-
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...
-
The properties of water and steam become identical at (a) 0.1 bar (b) 1 bar (c) \(100 \mathrm{bar}\) (d) 212.2 bar.
-
Steam from an engine exhaust at 1.25 bar flows steadily through an electric calorimeter and comes out at \(1 \mathrm{bar}, 130^{\circ} \mathrm{C}\). The calorimeter has two \(\mathrm{kW}\) heaters...
-
In thermodynamic analysis, a pure substance is that which (a) Consists of only a single chemical species (b) has no dissolved impurities (c) may have a number of chemical species but the composition...
Study smarter with the SolutionInn App