Correlation/Regression
The correlation of X and Y is r = 0.4. Is the correlation of Y and X then 0.4, -0.4, or -0.6?
0.4
At a certain college (which has 400 students), there is a Biology club and a Camping club. The Biology club has 20 members. The Camping club has 60 members, 3 of which are in the Biology club. At this school, is being in the Biology club independent of being in the Camping club?
Yes, independent.
Define X as the number of tires a truck driver gets replaced in a year. Is this a discrete random variable, continuous random variable, or not a random variable?
Discrete random variable
You calculate Pearson's r and the regression equation y -hat = mx + b for a collection of data. You know that r and m must have the same....
A. Sign
B. Magnitude
C. Sign and magnitude (i.e. they're the same number)
A
I have a thumbtack. If I drop it onto my desk, it either lands with the point facing up or not facing up. How can I assess the probability of the thumbtack landing face up, and what type probability would I be using?
Drop the tack on your desk several times. Count how many times it lands face up and divide that by the number of times you dropped the tack. This is frequentist probability.
A bag is full of marbles: 10 red, 10 blue, and 10 green. You draw five marbles (without putting them back) and count how many reds you get. Does the number of reds you get represent a binomial random variable? If so, what are n and p? If not, say why not.
No, the probability of success p is changing each time! In other words, each draw is not independent of the previous one.
The regression equation BloodPressure-hat = 42.3 + 0.49*Stress uses someone's stress level to predict their blood pressure. In one sentence, interpret the 0.49.
"A one point increase in the stress test is associated with a 0.49 increase in blood pressure."
A bag is filled with marbles: 5 yellow and 5 green. You draw two marbles at random. What's the probability that at least one of them is yellow?
P(Y1 U Y2) = P(Y1) + P(Y2) - P(Y1 and Y2) = P(Y1) + P(Y2) - P(Y1)*P(Y2|Y1) = 5/10 + 5/10 - (5/10)*(4/9) = 0.778
You roll a six sided die 20 times. What’s the probability of getting exactly three 6’s?
23.79% (use the binomial formula)
We find that the correlation between educational level attained and yearly income is r = 0.72. This finding must mean that....
A. higher education causes people to make more money.
B. lower income is associated with higher educational level.
C. people with lower educational levels tend to have lower incomes.
D. people with higher educational levels tend to have lower incomes.
C
In a certain course, 37% of the students are athletes. Of the athletes, 73% would prefer to win an Olympic gold medal over a Nobel Prize. Of the non-athletes, 31% would prefer to win a gold medal over a Nobel Prize. What's the probability that a student chosen at random from the class would prefer Olympic gold over a Nobel Prize?
P(G) = P(A)*P(G|A) + P(A')*P(G|A') = 0.37*0.73 + 0.63*0.31 = 0.4654
A charitable organization is running a raffle as a fundraiser. They sell 1000 tickets. There are ten third-prize tickets, two second-prize tickets, and a grand-winner ticket. A third-prize ticket gets you $20, a second-prize one gets you $100, and $500 goes to the grand winner. You buy a ticket. How much do you expect to win?
$0.90