Question 1

Choose the right formula for a simple linear regression

Accepted Answer

Y=β_1+β_2 X

Answer

lnY=β_1+βlnX

Answer

Y=A∙X^β

Answer

Y=β_1+β_2 X+β_3 X^2

Question 2

In the regression line Y=β_1+β_2 X+ε   what does coefficient β_1 represent?

Accepted Answer

intercept with y-axis

Answer

slope of the regression line

Answer

error of prediction

Answer

average distance to the mean

Question 3

In the regression line Y=β_1+β_2 X+ε  what does coefficient β_2 represent?

Accepted Answer

slope of the regression line

Answer

error of prediction

Answer

intercept with y-axis

Answer

average distance to the mean

Question 4

In the regression line Y=β_1+β_2 X+ε  what does ε represent?

Accepted Answer

error of prediction

Answer

intercept with y-axis

Answer

slope of the regression line

Answer

average distance to the mean

Question 5

In the regression line Y=β_1+β_2 X+ε  what does Y mean?

Accepted Answer

dependent variable (regressand)

Answer

independent variable (regressand)

Answer

independent variable (regressor)

Answer

dependent variable (regressor)

Question 6

In the regression line Y=β_1+β_2 X+ε  what does X mean?

Accepted Answer

independent variable (regressor)

Answer

dependent variable (regressand)

Answer

independent variable (regressand)

Answer

dependent variable (regressor)

Question 7

From the theoretical regression model  Y=β_1+β_2∙X+ε  it follows that Y is dependent on:

Accepted Answer

a regressor X and an error ε

Answer

an error ε

Answer

none of them

Answer

a regressor X

Question 8

In which analytical situations it is better to apply a linear regression?

Accepted Answer

estimate a relationship between price and space of flats

Answer

determine factors that influence the  choice of a job

Answer

determine causality between education and life expectancy

Answer

estimate a relationship between production cost and output

Question 9

In a multiple linear regression:

Accepted Answer

one dependent variable is explained by a set of independent variables

Answer

one independent variable is explained by a set of dependent variables

Question 10

The population regression line is the mean of Y as a function of the value of X.

Accepted Answer

True

Answer

False

Question 11

The estimators of the intercept and slope that minimize the sum of squared errors are called:

Accepted Answer

ordinary least squares (OLS) β-estimators

Answer

least absolute deviations (LAD) β-estimators

Answer

weighted least squares (WLS)  β-estimators

Answer

generalized least squares (GLS)  β-estimators

Question 12

Least squares regression line:

Accepted Answer

best fits the data in the sense of minimizing the sum of  squared errors

Answer

best fits the data in the sense of maximizing the sum of  squared errors

Question 13

The OLS regression line is also called sample regression line.

Accepted Answer

True

Answer

False

Question 14

The OLS regression line is also called sample regression function.

Accepted Answer

True

Answer

False

Question 15

The OLS estimator chooses the regression coefficients so that the estimated regression line is as close as possible to the observed data.

Accepted Answer

True

Answer

False

Question 16

The residual (ε) for the i-observation is the difference between Y_i and its predicted value.

Accepted Answer

True

Answer

False

Question 17

The OLS  β(hat)-estimators are sample counterparts of the population β-coefficients

Accepted Answer

True

Answer

False

Question 18

OLS is the dominant method used in practice.

Accepted Answer

True

Answer

False

Question 19

What is Residual Sum of Squares (RSS)?

Accepted Answer

the sum of the squared OLS residuals

Answer

the sum of squared deviations of the predicted values of Y from their average

Answer

the sum of squared deviations of Y from its average

Question 20

What is Explained Sum of Squares (ESS)?

Accepted Answer

the sum of squared deviations of the predicted values of Y from their average

Answer

the sum of the squared OLS residuals

Answer

the sum of squared deviations of Y from its average

Question 21

What is the Total Sum of Squares (TSS)?

Accepted Answer

the sum of squared deviations of Y from its average

Answer

the sum of the squared OLS residuals

Answer

the sum of squared deviations of the predicted values of Y from their average

Question 22

The standard error of the regression is an estimator of the standard deviation of the regression error.

Accepted Answer

True

Answer

False

Question 23

Regression errors are observed parameters.

Accepted Answer

False

Answer

True

Question 24

OLS Assumption 1: The expected value of residuals (ε) is equal to zero for all observations.

Accepted Answer

True

Answer

False

Question 25

OLS Assumption 2: The variance of each residual is constant for every observation.

Accepted Answer

True

Answer

False

Question 26

OLS Assumption 3: Residuals are uncorrelated between observations.

Accepted Answer

True

Answer

False

Question 27

OLS Assumption 4: Residuals (ε) are independent on explainable variables (regressors)

Accepted Answer

True

Answer

False

Question 28

OLS Assumption 5: Model is linear in relation to its parameters.

Accepted Answer

True

Answer

False

Question 29

If OLS assumption hold then in large samples the OLS estimators have sampling distributions that are normal.

Accepted Answer

True

Answer

False

Question 30

Large-sample normal distribution lets us develop methods for hypothesis testing and constructing confidence intervals using the OLS estimators.

Accepted Answer

True

Answer

False

Question 31

OLS, just like the sample mean, can be sensitive to large outliers.

Accepted Answer

True

Answer

False

Question 32

OLS estimators are computed from a randomly drawn sample.

Accepted Answer

True

Answer

False

Question 33

Gauss-Markov theorem: When the set of OLS assumptions hold, then OLS estimators possess good qualities:

Accepted Answer

unbiased, consistent, efficient

Answer

unbiased, inconsistent, efficient

Answer

unbiased, consistent, inefficient

Answer

biased, consistent, efficient

Question 34

β-estimators are unbiased:

Accepted Answer

on average, β-estimators fall into unknown population β-coefficients

Answer

when the sample size is large β-estimators will be close to the true population β-coefficients with high probability

Question 35

β-estimators are consistent:

Accepted Answer

when the sample size is large β-estimators will be close to the true population β-coefficients with high probability

Answer

on average, β-estimators fall into unknown population β-coefficients

Question 36

β-estimators are efficient:

Accepted Answer

variance of β2-estimator is the least as it could be

Answer

when the sample size is large β-estimators will be close to the true population β-coefficients with high probability

Answer

on average, β-estimators fall into unknown population β-coefficients

Question 37

The normal approximation to the sampling distribution of β-estimators is a powerful tool, because we are able to develop methods for making inferences about the true population values of the regression coefficients using:

Accepted Answer

only a sample of data

Answer

a sample which is not random

Answer

only two random samples

Question 38

The size of the linear correlation coefficient (r) indicates the strength of the linear relationship between X and Y. If r is near either 1 or −1 then the linear relationship between x and y is:

Accepted Answer

strong

Answer

we can not make a conclusion

Answer

weak

Question 39

What does a coefficient of determination (R^2) measure?

Accepted Answer

proportion of the variability in Y that is accounted for by the linear relationship between X and Y

Answer

causality between the dependent and independent variables

Answer

measure of spread in the data

Answer

sum of squared errors

Question 40

A 95% two-sided confidence interval for the population mean is an interval constructed so that it contains the true value of the population mean in 95 % of all possible random samples.

Accepted Answer

True

Answer

False

Question 41

Significance level is:

Accepted Answer

type I error

Answer

type II error

Question 42

Significance level (type I error) is:

Accepted Answer

the probability of rejecting the null hypothesis given that it is true

Answer

the probability of rejecting the null hypothesis given that it is false

Question 43

Type II error occurs when:

Accepted Answer

the null hypothesis is false but fails to be rejected

Answer

the null hypothesis is true but it is rejected

Question 44

The goal of a statistics test is to determine:

Accepted Answer

if the null hypothesis can be rejected

Answer

if the alternative hypothesis can not be rejected

Answer

if the null hypothesis can not be rejected

Answer

if the alternative hypothesis can be rejected

Question 45

After testing a hypothesis we can make a statistical inference that:

Accepted Answer

H0 is not rejected

Answer

H(a) is rejected

Answer

H0 is not accepted

Answer

there is no right answer

Question 46

Using critical value approach, a null hypothesis (H0) is rejected when:

Accepted Answer

t-statistic more than t_critical

Answer

t-statistic equal to t_critical

Answer

t_critical does not exist

Answer

t-statistic less then t_critical

Question 47

Using probability value (p-value) approach, a null hypothesis (H0) is rejected when:

Accepted Answer

p-value less than level of significance

Answer

p-value more than level of significance

Answer

p-value does not exist

Answer

p-value equal to the level of significance

Question 48

t-distribution is a member of a family of continuous probability distributions which describes:

Accepted Answer

samples drawn from a full population

Answer

full population

Question 49

t-distribution is:

Accepted Answer

symmetric

Answer

asymmetric

Question 50

Simple random sampling is the scheme in statistics when n objects are selected at random from a population and each of them is equally likely to be included in the sample.

Accepted Answer

True

Answer

False

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