CW #6 Autograder: Maximum Likelihood and Logit

Answer each question and click “Check”. When finished, download your completion PDF.

Score: 0 / 13
1) Maximizing a function

Find the \(x\) value where the function is at its maximum by taking the first derivative and setting it equal to 0.

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2) Log rules: simplify \(\log(xy^3)\)

Choose the correct simplification of \(\log(xy^3)\).

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3) Derivative: \(\log(1-x)\)

Find the derivative of \(\log(1-x)\) (assume \(\log\) is base \(e\)).

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4) Sample mean for 0/1 outcomes

Calculate the sample mean if a "heads" gives you 1 (success) and a "tails" gives you 0.

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5) Log-likelihood algebra

Simplify \(LL=\log(p^{15}(1-p)^5)\).

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6) Derivative of the log-likelihood

Take the derivative of \(LL\) from Question 5.

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7) MLE for \(p\)

Set the derivative from Question 6 equal to zero and solve for the value of \(p\) that maximizes \(LL\).

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8) Odds

Suppose a contestant has probability \(p=0.2\) of winning. Compute their odds \(\frac{p}{1-p}\).

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9) Log-odds

Using the same \(p=0.2\), compute \(\log\left(\frac{p}{1-p}\right)\).

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Rounded answers are accepted.

10) Log-likelihood function line (code)

Fill in the blank so that the function outputs the log likelihood for a guess for \(\beta_0\) and \(\beta_1\).

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Use log exactly. Spaces do not matter.

11) maxLik call (one token)

Fill in the blank to get maxLik to estimate \(\beta_0\) and \(\beta_1\) for us in the logit.

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12) Estimated coefficients

What did you estimate \(\beta_0\) to be? What did you estimate \(\beta_1\) to be?

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Rounded answers are accepted.

13) Predicted probabilities

Find the predicted probabilities that someone wins who is 0, 1, 28, 29, 50, and 51 years old.

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Rounded answers are accepted.