Assume we want to train the parameters of linear regression using gradient descent. Assume the training datahas two attributes 1, 2 and one target variable y. The data is given as (x1, x2, y). Find the updated parametersafter one step of gradient descent with a learning rate of 0.01. Initial parameters are w₁ = 0.5, W₂ = 0.5, andb = 0. Traning data is [(1,2,3), (2,3,5), (3,4,6)] and we are using the following regularized loss function:N1| || ||³2 + + Σ } / (√w x6 (x¹) — 3²) ²2Ni=1Show all of your calculations (including taking the derivative of the regularized loss function).

ANSWER: We are given the training data and initial parameters as: Training data: [(1,2,3),…

Answered: Assume we want to train the parameters…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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We collected teacher ratings for 25 courses taught by an instructor over a six-vear period. The students' ratings of the instructor are on a scale of 1 to 9. We found that The linear regression equation is: Average Rating = 7,88 -0.068 Numher of Students 1. Interpret the slope of this model including units: The average rating decreases per each additional student 0.068 ed teacher rating for a class size of 15 students using the given 7.88 prediction equation is Next page CS Scanned with CamScanner
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Independent variable data is listed in cells B2 through B100, and dependent variable data is in cells C2 through C100. Which spreadsheet function would calculate the slope of a linear regression model of this data? Group of answer choices =SLOPE(B2:B100,C2:C100) =SLOPE(C2:C100,B2:B100) =SLOPE(B2,C2) =SLOPE(C2,C100,B2,B100)
A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables? A positive linear relationship (r close to 1) A positive linear relationship (r close to -1) A negative linear relationship (r close to 1) A negative linear relationship (r close to -1)…
We are given the following training examples: (1.2, 3.2), (2.8, 8.5), (2,4.7), (0.9, 2.9), (5.1, 11) We want to apply a 3-nearest neighbor rule in order to perform regression. (a) : Predict the label (real value) at each of the following two points: 1 = 1.5 and x2 = 4.5. time we want to perform distance-weighted nearest neighbor regression. What values do we predict now for x1 = 1.5 and x2 = 4.5? (b). Instead of weighing the contribution of each of the 3 nearest neighbors equally, this
For10 observations on supply (X) and price (Y) the following data are obtained ΣΧ-130, ΣΧ-2280, ΣΥ-5506 , ΣΧΥ-3467, ΣΥ-220 Obtain regression line Y on X and estimate supply when price is 16.
Find the multiple regression equation with weight as the response variable and the dummy variable of sex and the variable of age as the explanatory variables.
You are given the following data, where X1 (final percentage in math class) and X2 (number of absences) are used to predict Y (standardized math test score in third grade): Y X1 X2 345 70 390 80 1 370 75 4 375 92 400 82 350 70 3 310 61 5 420 80 375 88 3 410 72 1 485 99 300 65 7 Determine the following multiple regression values. Report intercept and slopes for regression equation accurate to 3 decimal places: Intercept: a = Partial slope X1: bị = Partial slope X2: bz = Report sum of squares accurate to 3 decimal places: SSreg Test the significance of the overall regression model (report F-ratio accurate to 3 decimal places and P-value accurate to 4 decimal places): F-ratio = P-value = Report the variance of the residuals accurate to 3 decimal places: Sres = Report the results for the hypothesis test for the significance of the partial slope for final percentage in math class (report the test statistic for the regression coefficients accurate to 3 decimal places and P-value accurate to…
***PLEASE INCLUDE EXCEL OUTPUT WITH YOUR RESPONSE
Let x be the size of a house (in square feet) and y be the amount of natural gas used (therms) during a specified period. Suppose that for a particular community, x and y are related according to the simple linear regression model with the following values. ? = slope of population regression line = 0.016 ? = y intercept of population regression line = −7 Question: Graph the population regression line by first finding the point on the line corresponding to x = 1,000 and then the point corresponding to x = 2,000, and drawing a line through these points.
A grocery store manager did a study to look at the relationship between the amount of time (in minutes) customers spend in the store and the amount of money (in dollars) they spend. The results of the survey are shown below. Time 10 8 6 13 19 18 27 10 7 Money 58 25 41 51 84 81 87 45 15 1. The equation of the linear regression line is: ˆyy^ = ______ +_____ xx (Please show your answers to two decimal places)
A particular article used a multiple regression model to relate y = yield of hops to x, = average temperature (°C) between date of coming into hop and date of picking and x, = average percentage of sunshine during the same period. The model equation proposed is the following. y = 415.11 – 6.6x1 – 4.50x2 +e (a) Suppose that this equation describes the actual relationship. What mean yield corresponds to a temperature of 20 and a sunshine percentage of 40? (b) What is the mean yield when the average temperature and average percentage of sunshine are 19 and 44, respectively?

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