Given that a linear regression model is fitted to a set of training data. If there exist some 0o, 01 such that J(0, 0,) = 0, what does it mean?

Linear regression aims to fit the parameters based on the training set T.x = 1, 2,...,m} so that the hypothesis function he (x) ...... + Onxn can better predict the output y of a new input vector x. Please derive the stochastic gradient descent update rule which can update repeatedly to minimize the least squares cost function J(0). D = {(x(i),y(¹)), i 00+ 01x₁ + 0₂x₂+... = =

Q4. Suppose our system is learning to recognize puppies and kittens from 80x80 pixel RGB images. Let x be a vector storing the pixel intensity values of the three color components for all the pixels. (a) If we train a logistic regression system with only the terms x as features, how many features do we have? (b) If we train a logistic regression system with all the quadratic terms (x;x;) as features, how many features do you have?

The following figure depicts the decision boundary for the logistic regression model built to predict preference for light beer vs. regular beer (PREFERENCE = Light is the success or positive class). The explanatory variables are INCOME and AGE. INCOME has a positive coefficient and AGE has a negative coefficient. Predictions are made based on the depicted decision boundary. Four observations are circled. Match them with the appropriate descriptions. Age (in years) A B C D 100 80 60 20 0 -20 SE $10 $20 $30 Beer Preference $40 $50 $60 $70 Income (in US$ thousands) L.I.TJ False negative True positive True negative False positive $80 LA $90 Regular ● Light

How do I create a function in python that will calculate the negative log likelihood for a Gaussian model with respect to mean and also variance. Please use data = [10, 25, 10, 8, 8, 9, 10, 22, 12, 13, 15, 4, 8, 9] as the distribution.

1. Let X~ Normal(, a²). Generate 5 samples of size 10,000 each for X. Compute the sample variance in each sample. Observe the values of the sample variances. What do you see? 2. Repeat problem 1 but with X~ Uniform(a, b). (Also note what the population variance is in this case).

In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…

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Please help with artificial intelligence questuon below If given a number of data samples from pairs of values ​​(x, y) namely {(0, 12), (1, 19), (2, 29), (3, 37), (4, 45)} (1) Make a data plot from the given sample where the vertical axis is the y value and the horizontal axis is the x value. (2) Given a simple regression model: y = a x + b where a, b are constant numbers. Use the given data sample and least square method to predict constants a and b from the regression model. (3) Using the predicted regression model in question (2) above, calculate the estimated value of y if the value of x = 7.

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