Love Island lm() Project Autograder

Check each answer as you go. The page will only show Correct or Incorrect. When you are done, download a completion PDF.

Groupmates present (one per line)

If you worked alone, put your name on the first line.

Question 1: Statistics Review

Scenario: a lottery ticket has a 90% chance of winning nothing and a 10% chance of winning $1000.

1(a)

What are the potential outcomes? (Fill in both blanks.)

Outcome 1

Outcome 2

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1(b)

What are the probabilities of each outcome? (Fill in both blanks.)

Probability of winning $0

Probability of winning $1000

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1(c)

What is the expected value? $E[X] = \sum_i x_i p_i$.

Expected value

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1(d)

What is the variance? $\mathrm{Var}(X) = \sum_i (x_i - E[X])^2 p_i$.

Variance

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1(e)

You buy 20 tickets and win $1000 one time out of 20. What is your estimate of the expected value (sample mean)?

Estimated expected value

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1(f)

Based on your 20 tickets, what is your estimate of the variance? Use $\frac{1}{n-1}\sum_i (x_i - \bar{x})^2$.

Estimated variance

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1(g)

Fill in each blank.

t statistic

The t statistic is _____ than $-2.093$ (type: less or greater)

This means we _____ the null (type: reject or fail to reject)

Our sample mean is only _____ standard error(s) away from $100$

This is (type: unusual or not unusual)

Conclusion: the true expected value may indeed be _____

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Question 2: Dplyr

2(a)

Out of the three seasons, how many people won (got third place, runner up, or winner)?

Numeric answer

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2(b)

What is the minimum, maximum, and median age of contestants?

Min age

Max age

Median age

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2(c)

Are male contestants, on average, older than female contestants?

Type: yes/no

Female median age

Male median age

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2(d)

What are the three most common professions among contestants?

Profession 1

Profession 2

Profession 3

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2(e)

Two most common professions for female contestants and two for male contestants.

Female: profession 1

Female: profession 2

Male: profession 1

Male: profession 2

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2(f)

What region of the UK are most of the contestants from?

Type the region

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Question 3: ggplot2

Paste the code you used to draw the plot.

Code

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Question 4: lm and hypothesis tests

4(a)

Paste the code you used to fit the model.

Code

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4(b) Interpretation

Fill in the blanks.

Baseline probability at age 0 (intercept)

This is (type: valid or not valid) as a probability

Probabilities should be between ____ and ____

Why can linear probability models give invalid probabilities? (type a short phrase)

A one year increase in age changes win probability by

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4(b) Hypothesis test for age

t statistic for age

This is (type: greater/less) than 1.985

Decision (type: reject/fail to reject)

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4(c) lm: day_joined

Fill in the blanks.

Model formula

Baseline probability at day 0 (intercept)

This (type: is/is not) a valid probability

Slope sign (type: increases/decreases)

Slope magnitude

p-value for day_joined

Decision (type: reject/fail to reject)

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Overall

Score: Not graded

Timestamp: Not graded

The completion PDF is a bullet summary of what you learned in this assignment.