Problems

1. (5 points) Textbook problem 2.1
2. (5 points) Textbook problem 2.2
3. (5 points) Textbook problem 2.3
4. (10 points) Show that $\text{corr} (\{(x+c, y)\}) = \text{corr} (\{(x,y)\} )$, by substituting into the definition. You'll need to use the properties of the mean and standard deviation.
5. (10 points) Show that $\text{corr} (\{(kx, y)\}) = \text{sign}(k) \text{corr} (\{(x,y)\} )$ for $k \neq 0$, by substituting into the definition. You'll need to use the properties of the mean and standard deviation. Note that $\text{sign}(k)$ is defined as follows: $$\text{sign}(k) = \left\{\begin{aligned} -&1 && \text{if } k < 0\\ &1 &&\text{if } k > 0 \end{aligned} \right.$$
6. (15 points) Textbook problem 2.8 (data). Note that US state abbreviations were not standardized until 1963. This data is from 1960, so NE=Nevada and NB=Nebraska. Here's how to annotate points in a scatter plot with matplotlib.