Lots of Details on Least Squares Linear Regression & XLMiner Analysis Toolpak in a Spreadsheet
Use Fit on Mathematica to find least squares linear regression line & graph SSE(b0,b1) (it's minimized). Then use XLMiner Analysis Toolpak to get regression output in a spreadsheet (can be done using Excel on a PC). Interpret the output and confirm various formulas. https://amzn.to/3Hd7tFN (Probability and Statistics with Applications, a Problem-Solving Text) Probability and Statistics Class, Fall 2021 Links and resources =============================== 🔴 Subscribe to Bill Kinney Math: https://www.youtube.com/user/billkinn... 🔴 Subscribe to my Math Blog, Infinity is Really Big: https://infinityisreallybig.com/ 🔴 Follow me on Twitter: / billkinneymath 🔴 Follow me on Instagram: / billkinneymath 🔴 You can support me by buying "Infinite Powers, How Calculus Reveals the Secrets of the Universe", by Steven Strogatz, or anything else you want to buy, starting from this link: https://amzn.to/3eXEmuA. 🔴 Check out my artist son Tyler Kinney's website: https://www.tylertkinney.co/ (0:00) Topic: Linear regression (0:28) Enter data on Mathematica (use Transpose too) (1:56) Find regression line with "Fit" on Mathematica (3:15) Regression SSE is minimized for the least squares linear regression line (5:59) Why it is called least squares linear regression? (7:00) Graph SSE(b0,b1) using Plot3D in Mathematica (9:57) Partial derivatives of SSE(b0,b1) (11:06) Solve for critical points with Mathematica's Solve command (13:23) Other methods could be used, but they would be more complicated (15:29) XLMiner Analysis Toolpak Add-On in a spreadsheet (25:41) Intercept and slope of the regression line in the output (27:35) Confirm the answers with formulas (33:41) Confidence interval to estimate β1, the population slope (39:22) Population regression line (40:44) Answer for the 95% confidence interval and margin of error (46:09) T statistic for hypothesis test on H0: β1 = 0 (49:29) Regression standard error S (50:02) Sum of squares SSxx (sum of squared deviations of the x values from their mean) (55:42) Alternative way to find SSxx using the standard deviation of the x's (58:29) Typos in the textbook (59:28) Find S using SSE, the sum of the squares of the residuals (sum of squares of "errors") (1:00:05) SSE using squared residuals (1:04:06) Observed value of s, the regression standard error (1:04:58) Confirm T-stat value (1:06:09) P-value of test H0: β1 = 0 vs H1: β1 ≠ 0 (two-sided alternative) (1:07:26) Practical conclusions (1:08:06) Standard error of B1 (an estimate for the standard deviation of the sampling distribution of B1) (1:09:12) Everything is based on the regression model and various derivations (for the distribution of the sample slope statistic B1) (1:10:10) What you need to know for HW and the Final Exam AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.