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SOLVED: Write down the expression for the negative log-likelihood of data (V1 JJn) under the exponential regression model with predictor matrix X of size n X p, coefficient vector Î², and intercept Î²â‚€. [2 marks]Find the expressions for the gradient of the negative log-likelihood with respect to the intercept Î²â‚€ and the coefficients Î²â‚, Î²â‚š. [4 marks]

SOLVED: Write down the expression for the negative log-likelihood of data (V1 JJn) under the exponential regression model with predictor matrix X of size n X p, coefficient vector Î², and intercept Î²â‚€. [2 marks]Find the expressions for the gradient of the negative log-likelihood with respect to the intercept Î²â‚€ and the coefficients Î²â‚, Î²â‚š. [4 marks]

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SOLVED: Consider fitting an intercept-only logistic regression model:logit[P(Y = 1|x)] = Î²â‚€Derive the MLE of Î²â‚€: Note: the intercept-only logistic regression model does have a closed form solution.Hint: think about what the equation of Î²â‚€ is for an intercept-only model. Plug this into the log-likelihood equation we derived in class and solve from there.Please show all supporting work.

SOLVED: Consider fitting an intercept-only logistic regression model:logit[P(Y = 1|x)] = Î²â‚€Derive the MLE of Î²â‚€: Note: the intercept-only logistic regression model does have a closed form solution.Hint: think about what the equation of Î²â‚€ is for an intercept-only model. Plug this into the log-likelihood equation we derived in class and solve from there.Please show all supporting work.

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