Regression, Correlation and Hypothesis Testing

Question 1

Linear regression with coding data

Answer 1

Substitute the coding formulas into the given equation and rearrange

Question 2

Regression line of x on y

Answer 2

x = my + c

Question 3

Finding PMCC or regression line on calculator

Answer 3

Stat
Type data into table
Graph
Click calc and X
ax+b
a and b are given, r is PMCC

Question 4

PMCC range

Answer 4

|r| <= 1

1 is a straight line with positive gradient, -1 with negative gradient

Question 5

PMCC Hypothesis testing test statistic

Answer 5

r - the calculated PMCC of the sample

Question 6

PMCC Hypothesis testing parameter

Answer 6

ρ - the PMCC of the population

Question 7

PMCC Hypothesis testing null hypothesis

Answer 7

H0 - always that ρ = 0

State whether one tailed or two tailed

Question 8

PMCC Hypothesis testing one-tailed vs two-tailed

Answer 8

One tailed is testing for positive or negative correlation specifically (ρ>0 or ρ<0)
Two-tailed is testing that there is a correlation (ρ != 0)

Question 9

PMCC Hypothesis testing alternative hypothesis

Answer 9

H1 - ρ > 0 or ρ < 0 (one-tailed) or ρ != 0 (two-tailed)

Question 10

Hypothesis testing significance level

Answer 10

α - the percentage chance that there isn’t a correlation

Will be decimal in the formula book
Half for two-tailed

Question 11

Hypothesis testing method

Answer 11

note n, r, H0, H1, α, critical value and whether one or two-tailed
Compare r to critical value for n and α in formula book table
Make conclusion

Question 12

Hypothesis testing conclusion

Answer 12

Compare r to α, state if there is enough evidence to reject H0 and state the significance level

Question 13

Critical region

Answer 13

The set of all values of the test statistic that would cause you to reject the null hypothesis

Question 14

Binomial hypothesis testing (one-tailed)

Answer 14

let p = the probability of success
H0: p = what the probability should be
H1: p > or < what it should be
Let X be the number of successes
X~B(n,p)
p = P(x<= or >= actual value)
α = significance level
if α > p, we can reject H0 at the significance level

Question 15

Two-tailed binomial hypothesis test

Answer 15

Half the significance level
Find np for the significance level and use P(X<=expected value) if the number you are checking is less than that, otherwise P(X>=expected value)

Question 16

One-tailed binomial critical region

Answer 16

Find the two values of x around the probability being α or 1 - α and use the one that would cause you to reject the null hypothesis

Question 17

Two-tailed binomial critical region

Answer 17

Carry out a one-tailed for α and 1-α, choosing the probability closest to α and 1-α
For upper tail use X >= x+1
New significance level is adding up each probability