**QUESTION 1**

We model the salary of the average inhabitant of Pinkland. Salaries are a function of education (expressed in years), working hours (expressed in hours), firm sales (expressed in millions of pinkies) and sector. There are 3 sectors in Pinkland, namely agriculture, industry and service.

Salaries are expressed in pinkies (currency of Pinkland). The model is estimated as follows:

Log(salary) = 1.2 + 0.166*educ + 0.76*log(hours) + 0.16*log(sales) + 0.35*service –

0.13*agriculture

N=800

R2 = 0.63

1) Interpret the coefficient on education. What type of relationship is this?

2) Interpret the coefficient on “hours” and “sales”. What type of relationship are these?

3) What is the base category for the categorical variable?

4) Interpret the coefficient on “service” and “agriculture”.

5) Calculate the degrees of freedom for the regression and explain if standard normal critical values can be used or not.

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**QUESTION 2**

Use the dataset: Energy.RData,

Use R to run a cross sectional regression on energy use per capita for the listed countries as follows:

lntpes_pc = 𝜷𝜷𝟎𝟎 + 𝜷𝜷𝟏𝟏𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟐𝟐𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟑𝟑𝐥𝐥𝐧𝐧𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠𝐠 + 𝜷𝜷𝟒𝟒𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟𝐟 + 𝜷𝜷𝟓𝟓𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝜷𝜷𝟔𝟔𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥𝐥 + 𝒖𝒖

The variables are defined as follows:

lntpes_pc = log of total primary energy consumption per capita (ktoe)

lnypcpenn =log of GDP per capita (USD)

lnypcpenn2 = square of log of GDP per capita (USD)

ln_gasprice = log of pump price for gasoline (USD/liter)

ln_annualprecip= log of annual precipitation (mm)

ffrents = Fossil Fuel Rents (% of GDP)

lnpop = log of population (in millions)

lnland = log of land area (in km2)

I_Incomegroup = refers to income groups “1” , “2” and “3”, low, mid and high income countries.

*”Log” always refers to natural logs or “ln” here.

1) Present your regression results in a table below (R output):

2) Interpret the constant and its p-value.

3) Interpret the coefficient on gas price and its p-value.

4) Interpret the coefficient on ln land and carry out (meaning: calculate with the official formula) a t-test to determine the significance of the coefficient.

5) Interpret the coefficient on ff-rents and its p-value.

6) The above model belongs to the class of nonlinear equations. Calculate the turning point of the nonlinear relationship.

7) Is this a U-shaped or inverted U-shaped relationship?

8) Interpret the adjusted R2 of the regression. `

9) a) Please define MLR 3 and describe if MLR 3 is likely to hold or not?

b) Please define MLR 4 and describe if MLR 4 is likely to hold or not? What other variables might be in the error term?

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**FORMULA SHEET**

**Critical values for the standard normal distribution (z)**

**Formula for a t-statistic**

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