TENTAPLUGG

Question 1

What are properties of good estimators?

Answer 1

1. It is unbiased/validity. The expected value of the sample parameter is equal to the population parameter.
2. It is reliable/efficient. The estimator has an as small variance as possible. Generally decreases when sample size increases

Question 2

Which starting points for CI and hypothesis testing are approximate because of CLT (single population)?

Answer 2

Case 3 and Case 4

Question 3

What are the assumptions for Case 1 (single pop.)?

Answer 3

• Xi follows a normal distribution

- Sigma2 (pop. variance) is known.

Question 4

What are the assumptions for Case 2 (single pop.)?

Answer 4

• Xi follows a normal distribution

- Sigma2 (pop. variance) is UNknown

Question 5

What are the assumptions for Case 3 (single pop.)?

Answer 5

• Xi follows an unknown distribution
• Sigma2 is unknown
• n >= 30

Question 6

What are the assumptions for Case 4 (single pop.)?

Answer 6

• n >= 40

Question 7

What are the assumptions for Case 5 (single pop.)?

Answer 7

• Xi follows a normal distribution

- mew and Sigma2 are unknown

Question 8

Which starting points for CI and hypotheses testing are approximate (double populations)?

Answer 8

• Case 2 (round down v)

- Case 3 and Case 5, from CLT

Question 9

What are the assumptions for Case 1 (double pop.)?

Answer 9

• Independent samples
• Xi, Yj follows normal distributions
• mewX, mewY, Sigma2X, Sigma2Y are unknown, but Sigma2X=Sigma2Y–> pooled variance S2p

Question 10

What are the assumptions for Case 2 (double pop.)?

Answer 10

• Independent samples
• Xi, Yj follow normal distributions
• mewX, mewY, Sigma2X, Sigma2Y are unknown, Sigma2X & Sigma2Y are UNEQUAL

Question 11

What are the assumptions for Case 3 (double pop.)?

Answer 11

• Independent samples
• Xi, Yj follow unknown distributions
• mews and sigma2s are unknown (may or may not be equal)
• nx, ny >= 30

Question 12

What are the assumptions for Case 4 (double pop.)?

Answer 12

• DEPENDENT samples (matched pair)
• Xi, Yi follows normal distributions, –> Di follows normal distribution
• mews and sigma2s are unknown

Question 13

What are the assumptions for Case 5 (double pop.)?

Answer 13

• Independent samples

- nx, ny >=40

Question 14

What are the assumptions for Case 6 (double pop.)?

Answer 14

• Independent samples
• Xi, Yj follows normal distributions
• mews and sigma2s are unknown

Question 15

What is special about the CI for sigma2x/sigma2y (Case 6)?

Answer 15

The CI in the formula sheet is for sigma2Y/sigma2X, so switch order of x- and y-terms.

Fa;b;0,95 = 1 / Fb;a;0,05

Question 16

What are the four essential concepts of hypotheses testing?

Answer 16

1. A null hypothesis H0, and an alternative hypothesis H1
2. A significance level of the test, alpha
3. A test statistic
4. A decision rule

Question 17

What are the four possible scenarios of hypothesis testing?

Answer 17

1. P(Accept H0 I H0 is true) = 1-alpha
2. P(Accept H0 I H1 is true) = beta (type 2 error/false negative)
3. P(Reject H0 I H0 is true) = alpha (type 1 error/false positive)
4. P(Reject H0 I H1 is true) = 1-beta

Question 18

What is the power of a test (hypothesis testing)?

Answer 18

The ability to correctly reject H0 when it is false.

P(Reject H0 I H1 is true) = 1-beta

Question 19

What is the p-value (hypothesis testing)?

Answer 19

The smallest significance level alpha, at which H0 can be rejected.
General rule: Reject H0 if p-value < given alpha

Question 20

How can we test for correlations?

Answer 20

With the assumption that we have a random sample from a joint normal distribution, we can use Pearson’s test for correlations.

Question 21

What are the assumptions for the SLR model?

Answer 21

1. Linearity
2. The Xi values are fixed/known
3. E(error term i) = 0. V(error term i) =Sigma2(error term)
4. E(error term i ; error term j) = 0 (i not equal to j)
5. Error term i follows a normal distribution

Question 22

What is the residual?

Answer 22

e(i) = y(i) - y-hat(i).

Deviation between estimated value and observed value.

Question 23

What is S2(error term)?

Answer 23

An estimator of the error term.

Question 24

What parts does ANOVA consist of?

Answer 24

• SST: sum of squares total. variation in dependent variable.
• SSR: sum of squares regression. model variation
• SSE: sum of squares error. residual variation
• R2-value: how many percent of the variation in the data that are explained by the model. R2>0,5

FOR MLR:
- Adjusted R2-value. Protects against overfitting.

Question 25

What is the optimal predictor for both individual and aggregate/average predictions (SLR), and how do we find CIs?

Answer 25

y-hat(n+1) = b0 + b1*x(n+1)

individual: y-hat(n+1) +- t(alpha/2)(n-2) * s(e) * s(y-hat, n+1)
Aggregate: y-hat(n+1) +- t(alpha/2)(n-2) * s(e) * s(E(……))

Question 26

What are the assumptions of the MLR model?

Answer 26

1. Linearity
2. The x1i, … , xki values are fixed/known
3. E(error term i) = 0. V(error term i) =Sigma2(error term)
4. E(error term i ; error term j) = 0 (i not equal to j)
5. The independent variables (x) are not perfectly related (no multicollinearity problem)

FOR CI and HT
6. Error term i follows a normal distribution

Question 27

What is multicollinearity and how do we detect it?

Answer 27

Independent variables are perfectly related.

Signs of problem:

• R2 values are close to 1 but non/few of the variables are significant
• Spurious/wrong signs of coefficients

Detect:

• Sample correlation higher than ex 0,8?
• Variance Inflation Factor, VIF > 10?
• Tolerance factor: 1/VIF < 0,1?