Problems
- (5 points) Textbook problem 2.1
- (5 points) Textbook problem 2.2
- (5 points) Textbook problem 2.3
- (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.
- (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:
$$
\text{sign}(k) = \left\{\begin{aligned}
-&1 && \text{if } k < 0\\
&1 &&\text{if } k > 0
\end{aligned}
\right.$$
- (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.