You will establish a simple linear relationship on a (very small) subset of 5 countries: Table 1:
Question:
You will establish a simple linear relationship on a (very small) subset of 5 countries:
Table 1: GDP and Agricultural Labor Productivity, Five Countries
| Country | Labor Productivity in Agriculture (US$1000) | GDP per capita (US$1000) |
|---|---|---|
| Bulgaria | 15.03 | 4.73 |
| Croatia | 21.64 | 10.62 |
| Saudi Arabia | 24.31 | 17.71 |
| Spain | 33.20 | 25.38 |
| Italy | 47.90 | 30.13 |
(a) Estimate the linear relationship between GDP per capita and Labor Productivity in Agriculture, with Labor Productivity in Agriculture as your dependent variable. Calculate β(hat)0 and β(hat)1 for the five countries in Table 1. Show all intermediate calculations.
Equations:
β(hat)1=Sxy/Sx2 = Cov(x,y)/Var(x)
β(hat)0= ̄y − β(hat)1 ̄x
(b) Using appropriate and precise language, write 2–3 sentences interpreting the values of your estimates β(hat)0 and β(hat)1.
(c) Calculate the predicted Labor Productivity in Agriculture and the residual. Verify that the residuals sum to (approximately) zero.
(d) According to the model you’ve estimated, what is the predicted Labor Productivity in Agriculture for a country with a GDP per capita of $15,000?
(e) Again using your spreadsheet, calculate the R2 from your model. How much of the variation in Labor Productivity in Agriculture for these 5 countries is explained by their GDP per capita?
(f) Can you provide some reasons for why agricultural labor productivity might be lower in less developed countries?
(g) Repeat part (a) for a different subset of 5 countries:
Table 2: GDP and Agricultural Labor Productivity, Five Countries
| Country | Labor Productivity in Agriculture (US$1000) | GDP per capita (US$1000) |
|---|---|---|
| United Kingdom | 28.95 | 39.79 |
| Austria | 32.41 | 41.37 |
| Sweden | 38.24 | 45.26 |
| Denmark | 47.04 | 47.65 |
| Iceland | 72.56 | 57.63 |
(h) How do your estimates of β(hat)0 and β(hat)1 change between Tables 1 and 2? Briefly explain these changes in 3–5 sentences.
Expert Answer:
The detailed answer for the above question is provided below a To calculate hat1 and hat0 we need to calculate the covariance Sxy and variance Sx2 of GDP per capita and Labor Productivity in Agricultu... View the full answer
Statistics for Managers Using Microsoft Excel
ISBN: 978-0133130805
7th edition
Authors: David M. Levine, David F. Stephan, Kathryn A. Szabat
