Topic 1. Linear regression. OLS

Question 1

What is a population?

Answer 1

Population is a set of similar items or events. It is a group of actually existing objects or a hypothetical group of objects conceived as a generalization from experience.

Question 2

What is a sample?

Answer 2

Sample is a data set selected from a statistical population.

Question 3

What are the elements of a sample

Answer 3

observations (or sampling units, sampling points)

Question 4

What is the common aim of statistical analysis?

Answer 4

to produce information about the population of our interest

Question 5

What is the simple random sampling?

Answer 5

In the simple random sampling n objects are selected at random from a population and each object is equally likely to be included in the sample.

Question 6

What does “simple linear regression” mean?

Answer 6

The word “simple” means that y depends on only one variable x.

Question 7

What does the slope parameter in a regression line represent?

Answer 7

Slope of the line measures its steepness. It describes how y changes in response to a one unit change in x.

Question 8

What is the linear correlation coefficient?

Answer 8

The linear correlation coefficient (r) measures the strength and direction of the linear relationship between two variables.

Question 9

What is the standard deviation?

Answer 9

SD quantifies the amount of variation of values in a data set.
SD is simply the average distance to the mean.

Question 10

What does low standard deviation indicate?

Answer 10

Low SD indicates that the data points tend to be close to the mean

Question 11

What does high standard deviation indicate?

Answer 11

High SD indicates that the data points are spread out over a wider range of values.

Question 12

What is a statistical error?

Answer 12

Statistical error is the amount by which an observation differs from its expected value, based on the whole population, from which the observation was selected randomly.

Question 13

Is the statistical error observable parameter?

Answer 13

No. The statistical error is unobservable, because the population mean is unobservable.

Question 14

How the statistical error is measured?

Answer 14

Statistical error is the difference between the value of a variable in the sample and the unobservable population mean.

Question 15

What is a residual?

Answer 15

Residual is an observable estimate of the unobservable statistical error.

Question 16

How a residual is measured?

Answer 16

Residual is the difference between the value of a variable in the sample and the observable sample mean.

Question 17

What is the standard error?

Answer 17

The standard error (se) of a parameter is an estimator of its population standard deviation.

Question 18

If the population parameter is the mean, how is its standard error called?

Answer 18

If the parameter is the mean, it is called the standard error of the mean

Question 19

In statistical formulas, what does a parameter σ stand for?

Answer 19

σ stands for the population standard deviation

Question 20

In statistical formulas, what does a parameter ‘s’ stand for?

Answer 20

’s’ stands for the sample standard deviation