Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x). LinReg y=a+bx a = 2.22055585 b=0.338208 r=0.437979968 r 0.66180055 Part: 0/3 Part 1 of 3 Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers). Regression line equation: y =

Interpreting technology: The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x). LinReg y=a+bx a = 2.22055585 b=0.338208 r=0.437979968 r 0.66180055 Part: 0/3 Part 1 of 3 Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers). Regression line equation: y =

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data is Yi=−1.068+1.394Xi and the standard error of the estimate is SYX=19.412. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Significance level at 0.05 . Complete parts (a) and (b) below.
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data is Yi=−1.606+1.428Xi and the standard error of the estimate is SYX=19.348. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Complete parts (a) and (b) below. a. At the 0.01 level of significance, is there evidence of a linear relationship between online trailer views and opening weekend box office gross? Determine the hypotheses for the test. b. Construct a 95%confidence interval estimate of the population…
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data isYi=−0.914+1.408Xi and the standard error of the estimate is SYX=19.887. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model. Compute the test statistic.
At Hard Rock’s Moscow restaurant, the manager is trying to evaluate how a new advertising campaign affects guest counts. Using data for the past 10 months (see the table), develop a least-squares regression relationship and then forecast the expected guest count when advertising is $65,000.
A box office analyst seeks to predict opening weekend box office gross for movies. Toward this goal, the analyst plans to use online trailer views as a predictor. For each of the 66 movies, the number of online trailer views from the release of the trailer through the Saturday before a movie opens and the opening weekend box office gross (in millions of dollars) are collected and stored in the accompanying table. The least-squares regression equation for these data is Yi=−1.660+1.417Xi and the standard error of the estimate is SYX=19.349. Assume that the straight-line model is appropriate and there are no serious violations the assumptions of the least-squares regression model.
What is meant by the term least-squares regression?
Carbon dioxide (CO,) is produced by burning fossil fuels such as oll and natural gas, and has been connected to global warming. The following table presents the average amounts (in metric tons) of COy emissions for certain years per person in the United States and per person in the rest of the world. Use a TI-84 calculator to answer the following, (a) Compute the least-squares regression line for predicting U.S. emissions from non-U.S. emissions. Round the slope and y-intercept values to four decimal places.
In a regression based on 30 annual observations, U.S. farm income was related to four independent variables—grain exports, federal government subsidies, population, and a dummy variable for bad weather years. The model was fitted by least squares, resulting in a Durbin-Watson statistic of 1.29. The regression of e2i on ŷi yielded a coefficient of determination of 0.043.a. Test for heteroscedasticity.b. Test for autocorrelated errors.
A company trains its employees with instructional videos and claims that the amount of time, in hours, spent training is linearly related to an increase in productivity. The company selected a random sample of five employees to test its claim. The data were used to create the computer output for a least-squares linear regression, shown in the table. Variable DF Estimate SE Intercept 1 3.6 1.1489 Hours 1 0.8 0.3464 Which of the following is the correct test statistic and number of degrees of freedom? t=2.31 with 4 degrees of freedom A t=2.31 with 3 degrees of freedom B t=2.31 with 5 degrees of freedom C t=3.13 with 1 degree of freedom D t=3.13 with 3 degrees of freedom E
Kolmorogov-smirnov test T-test Mann-whitney Linear Regression Are these statistical analyses could be computed in SPSS automatically?
Using the least-squares regression line, y=-25.5+1.5x, what is the residual for the data point at (28,19)?