Imagine that you should conduct a small research on the relationship between the share of the retired people in a region and the turnout in the elections to the Russian State Duma (2011). It is observed that in Russia voters of the retirement age tends to participate in elections more actively than the younger generation. The question is: does the share of pensioners positively affect the turnout in elections?
To answer this question you are provided with the dataset containing the variables you need for the analysis. The share of pensioners (%) is the variable ret, and the turnout (%) is the variable turnout. You should use the least squares regression model in this task.
1.1. What is the dependent variable in your model?
1.2. What is the independent variable in your model?
1.3. Formulate the null hypothesis you are going to test.
1.4. Formulate the alternative hypothesis.
1.5. Run R commands to perform the simple least squares regression. Provide the code you use to do it.
1.6. Interpret the output you get. Your interpretation should include the answers for the following questions:
How does the turnout rate change when the share of pensioners in a region increases by one percentage point?
Can we conclude that the share of pensioners has a statistically significant association with the turnout rate? Do not forget to indicate the level of significance you make your conclusions at.
Is the model you performed plausible? Consider the output you got and use your own perception of the research described in this task.