... ... @@ -15,7 +15,7 @@ \begin{outline} \1 Today: How well does your data fit a line? \2 More complicated regressions exist, of course, but we'll stick with this one for now \2 Talk about linear in detail, look at some more complicated ones in R \2 Eyeballing is just not rigorous enough \1 Basic model: $y_i = b_0 + b_1x_i + e_i$ ... ... @@ -74,17 +74,6 @@ \3 For example: How sure are we that two slopes are actually different \2 \textit{When would we want to show that the confidence interval for $b_1$ includes zero?} \1 Confidence intervals for predictions \2 Confidence intervals tightest near middle of sample \2 If we go far out, our confidence is low, which makes intuitive sense \2 $s_e \big(\frac{1}{m} + \frac{1}{n} + \frac{(x_p - \overline{x}^2)}{\sum_{x^2} - n \overline{x}^2}\big)^\frac{1}{2}$ \2 $s_e$ is sttdev of error \2 $m$ is how many predictions we are making \2 $p$ is value at which we are predicting ($x$) \2 $x_p - \overline{x}$ is capturing difference from center of sample \2 \textit{Why is it smaller for more $m$}? \3 Accounts for variance, assumption of normal distribution \1 Residuals \2 AKA error values \2 We can expect several things from them if our assumptions about regressions are correct ... ... @@ -94,6 +83,11 @@ \2 Q-Q plot of error distribution vs. normal ditribution \2 Want the spread of stddev to be constant across range \1 Switch to R \2 Show example of linear fitting (good fit) \2 Show example of linear fitting (bad fit) \2 Show example of polynomial fit (intercept and 3 coefficients) \1 For next time \2 I won't be here week after spring break \2 papers3 due Tuesday of spring break week ... ... @@ -102,7 +96,8 @@ \2 lab2 now due Friday after spring break \3 I want some more from you now, so be sure to update your fork \3 Mainly, I want to know how you will improve the graph you are reproducing are reproducing, and to actually look a bit at the code you find \end{outline} ... ...