he table below contains data about the yearly unemployment rate and poverty rate for Free State Province for a period of 10 years (from 2010 - 2019). Assume that unemployment rate and poverty rate are normally distributed. NB: use the values as they appear in the data table to obtain all of your estimates. years 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Unemployment rate 3.5 4.4 5.2 2.8 3.9 4.0 3.8 3.3 4.8 3.1 Poverty rate 5.1 6.3 7.5 5.3 7.5 6.8 5.3 6.0 6.4 4.2 a. Use ordinary least squares (OLS) to fit the sample regression function (poverty rate)i=b0+b1(unemployment rate)i+ei to the data. Write down the estimated sample regression function and interpret your estimate of b1. b. Estimate and interpret the coefficient of determination, R^2. c. Does the poverty rate increase as unemployment increases? In other words, is the coefficient of unemployment rate (b1) positive? Test at the 5% level.
The table below contains data about the yearly unemployment rate and poverty rate for Free State Province for a period of 10 years (from 2010 - 2019). Assume that unemployment rate and poverty rate are
| years | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
| Unemployment rate | 3.5 | 4.4 | 5.2 | 2.8 | 3.9 | 4.0 | 3.8 | 3.3 | 4.8 | 3.1 |
| Poverty rate | 5.1 | 6.3 | 7.5 | 5.3 | 7.5 | 6.8 | 5.3 | 6.0 | 6.4 | 4.2 |
a. Use ordinary least squares (OLS) to fit the sample regression
b. Estimate and interpret the coefficient of determination, R^2.
c. Does the poverty rate increase as unemployment increases? In other words, is the coefficient of unemployment rate (b1) positive? Test at the 5% level.
d. Estimate a 90% prediction interval for poverty rate, if unemployment rate =4.
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