OLS Autograder (Q1 to Q9)

Group members present

List everyone in your group who is here today (one per line).

Answer all parts, then click “Check Q1”.

It still costs 30¢ to play, but the coin is not fair. Enter the probability of heads that makes the expected value exactly 30¢.

Let X take on values 0 through 4 with equal probability. Enter the expected value and the variance.

The sample is x <- c(1,1,1,2,2,2,2,3,3,3). Enter your estimates for E[X] and Var(X). Also paste the R code you used. Your code should use sum() and length().

Enter your values for b1 and b0, then paste the R code you used. Your code should use cov(), var(), and mean().

First paste the R code you used to fit the model. Then fill in the two interpretation blanks.

Answer parts (a) through (f), then click “Check Q7”.

Paste the exact R code you used to draw the plot:

(a) win ~ age

Use lm() to estimate the model win_i = β₀ + β₁ age_i + u_i. The baseline probability someone who is zero years old wins is , which (choose) is is not statistically significantly different from zero: the p-value (choose) is is not less than 0.05. A one year increase in age means someone's probability of winning increases by , which (choose) is is not statistically significantly different from zero.

(b) win ~ day joined

Use lm() to estimate the model win_i = β₀ + β₁ day joined_i + u_i. The baseline probability that someone who joins the show on day zero wins is , which (choose) is is not statistically significantly different from zero. A one day increase in day joined means someone's probability of winning (choose) increases decreases by , which (choose) is is not statistically significantly different from zero.