We worked on constructing residual plots by hand in order to understand the calculator-generated graphs. We focused on what a residual actually is, and why we want residuals to be as small in magnitude as possible when assessing a linear regression model.
We worked heavily with the the calculator to create scatter plots of paired data and then use the data pairs to calculate the coefficients of the least-squares regression line, then store and graph the equation in the same window as the scatter plot. We discussed how to assess how well the data pairs fit the regression line and how to use the correlation coefficient r.
Today we continued to work with using collected paired data to create a predictive model using the least-squares regression method. We focused on how to create a residual plot by using lists rather than using the built in residual function in the calculator and discussed how these plots relate to and differ from the scatter plot of the original paired data points with graph of the regression line, as well as how the residual plot should be interpreted.
Today we covered more on linear regression with focus on how to interpret results from the TI84 calculator as well as output generated by other statistical platforms such as Minitab. We made an effort to understand what the R-Sq value tells us about the usefulness of a given linear model. We spent some time reviewing and clarifying what it means to create a prediction model from collected data pairs and then to use that model to estimate future pairs.
Emma and I worked through examples. I explained how to use the calculator to construct a scatterplot and to then fit a Least Squares equation to the data and then graph it in the same window as the scatterplot. We also talked in detail about how to interpret these results.
We worked through problems from Emma's homework assignment that she had struggled with. These problems involved calculating and interpreting the correlation coefficient r. We worked on notation.
We discussed the meaning of the correlation coefficient r, and how to calculate it using built in function in the calculator, and also by hand with the aid of List Math. We watched a video online about correlation vs. causation.
