Introductory Statistics Homework #2B & 3

MAT 382  Homework for least squares started on: Friday, 2 Oct 2015 to be submitted on: Wednesday, 7 Oct 2015 Current Sections  Please submit your answers to the following problems:

o The data for this problem are the duration x of an eruption of Yellowstone National Park’s “Old Faithful” and the interval y until the subsequent eruption. Use the data from old faithful.xls (A) and these instructions: 1. Compute Pearson’s correlation coefficient. 2. Using r (from step #1) and the means & standard deviations for x & y, use your calculator ˆ ˆ to compute the values of the least squares slope 1 and intercept  0 . 3. Now use the regression command on your calculator or Minitab to obtain the equation of the least squares line for these data. Be sure its slope and intercept agree with your answers from #2. 4. Graph the least squares line on your scatterplot. Make sure it looks like a “good fit”.

o Do either the following skyscraper problem or Problem Z below. The data for this problem are the number of stories x of skyscrapers and their height y. Use the data from building heights.xls (B) and these instructions: 1. Use the regression command on your calculator or Minitab to obtain the equation of the least squares line for these data. 2. Print a graph showing your data and the least squares line. 3. Use your linear equation from #1 to estimate the height of Boston’s Prudential Tower. Compare your estimate to the actual height of “the Pru”. [Anybody else been atop the Pru?] 4. Obtain the value of the coefficient of determination R2.

o The data for this problem are the number of years x that a person has played a stringed instrument and their level of brain activity y. Use the data from violin.xls (C) and these instructions: 1. Use the regression command on your calculator or Minitab to obtain the equation of the least squares line for these data. 2. Print a graph showing your data and the least squares line. 3. What would your response be if you were asked to estimate the activity level for Andrés Segovia (renowned guitarist) at the time of his death? (Segovia died at age 94 and began to play the guitar at age 4.) 4. What percentage of variation in activity is explained by its linear relationship with years? What percentage is not explained…? o Problem Z 1. Derive the equations for the slope and for the intercept of the least squares line as fit to a general set of data. There are (at least) two approaches you might take. Do at least one but, for extra credit, do both. Either way, be sure to show that your estimates achieve a MINimum for the sum of squares collective “distance” between the datapoints and the line. . Use some Multivariable Calculus . Use some Linear Algebra Complete as of 20 May 2018