Statistical Methods for Economists – Week 3

                                       (Questions and Tasks)

The topic: Regression Analysis

1.) What is the aim of the regression analysis?

2.) Explain what kind of data we use in linear regression (qualitative, quantitative, ordinal,
linguistic…), what is a dependent variable and what an independent variable(s).

3.) Write down a formula for linear regression (both for one and more independent variables). How
do we call coefficients belonging to independent variables?

4.) What expresses the epsilon term?

5.) What is Pearson’s correlation coefficient R?

6.) Consider the data in the table below and use them for a linear regression (you can use Excel or
Gretl) to find out how spending on vacations depends on income.

a) What is the formula (equation) of linear regression?.........................

b) What is a coefficient of determination R^2? Find R^2 in this example:……………

c) Find Pearson’s correlation coefficient R:..,,,,,,,,,,..

d) Show the linear regression in a graph (copy-paste from Excel)

e) In Excel click on “Data”, then on “Analysis of data”, then select “Regression”. Excel provides
an output in a form of three tables. Learn what information is provided in each table, and find: i)
is the model (as a whole) statistically significant? ii) are both regression coefficients
statistically significant?

                                     Monthly income (x), Euros

                                                                                                  Vacation spending (y) Euros

                                               9500

                                                                                                              950

                                               6420

                                                                                                              770

                                               4300

                                                                                                              400

                                               3800

                                                                                                              410

                                               7100

                                                                                                              550

                                               8500

                                                                                                              750

                                               9200

                                                                                                              890