How can the standard error of estimate be interpreted?
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4Olympic 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?If your graphing calculator is capable of computing a least-squares sinusoidal regression model, use it to find a second model for the data. Graph this new equation along with your first model. How do they compare?
- The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y=47.271x+18,712.47. Issues, x Proceeds, y425 18,758468 29,602678 43,797478 31,661485 65,518396 65,33069 21,42764 11,847181 32,392157 27,561 Complete parts a and b. The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. The equation of the regression line is y=47.271x+18,712.47. Complete parts a and b. (a) Find the coefficient of determination and interpret the result. (Round to three decimal places as needed.) (b) Find the standard error of estimate se and interpret the result. (Round to three decimal places as needed.)The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings(in millions) are shown in the table. The equation of the regression line is y=47.538x+18,727.65. Complete parts a and b. Issues, x Proceeds, y 423 18,632 460 27,913 687 44,071 485 32,435 500 66,634 389 66,734 57 22,180 65 11,296 188 31,929 163 27,891 (a) Find the coefficient of determination and interpret the result. How can the coefficient of determination be interpreted? (b) Find the standard error of estimate se and interpret the result. How can the standard error of estimate be interpreted?The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 569.The equation of the regression line is y=32.409x+17,285.501. Issues, x 410 467 679 499 497 394 62 53 189 174 Proceeds, y 18,223 28,066 43,757 31,337 35,488 35,312 22,180 10,660 30,384 28,416 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 569. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest million dollars as needed. Type your answer in standard form where "3.12 million" means 3,120,000.) A. There is a 95% chance that the predicted proceeds given 569 issues is between $____ and $____. B. We can be 95% confident…
- A company that holds the DVD distribution rights to movies previously released only in theaters wants to estimate sales revenue of DVDs based on box office success. The box office gross (in Php millions) for each of 22 movies in the year that they were released and the DVD revenue (in Php millions) in the following year are shown below and stored in a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b c. interpret the meaning of the slope, in this problem d. predict the sales revenue for a movie DVD that had a box office gross of Php75 million..1The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.5 8.2 6.6 3.7 2.9 2.8 2.1 0.4 yy 13.6 11.2 9.3 7.2 6.7 6.4 6 4.3 xx = thousands of automatic weaponsyy = murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places)Determine the regression equation in y = ax + b form and write it below. A) How many murders per 100,000 residents can be expected in a state with 10.5 thousand automatic weapons?Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 10.8 thousand automatic weapons?Answer = Round to 3 decimal places.The money raised and spent (both in millions of dollars) by all congressional campaigns for 8 recent 2-year periods are shown in the table. The equation of the regression line is ModifyingAbove y=0.982x−9.080. Complete parts a and b. Money raised, x 472.2 669.3 734.5 783.9 794.4 1034.8 974.9 1202.2 Money spent, y 430.3 677.4 731.9 764.1 748.9 1023.2 942.4 1157.9 (a) Find the coefficient of determination and interpret the result. (Blank) (Round to three decimal places as needed.) How can the coefficient of determination be interpreted? A. The coefficient of determination is the fraction of the variation in money spent that can be explained by the variation in money raised. The remaining fraction of the variation is unexplained and is due to other factors or to sampling error. B. The coefficient of determination is the fraction of the variation in money spent that is unexplained and is due to other…
- We wish to predict the salary for baseball players (y) using the variables RBI (x1) and HR (x2), then we use a regression equation of the form yˆ=b0+b1x1+b2x2 HR - Home runs - hits on which the batter successfully touched all four bases, without the contribution of a fielding error. RBI - Run batted in - number of runners who scored due to a batters's action, except when batter grounded into double play or reached on an error Salary is in millions of dollars.For these (x,y) pairs of data points: 1,5 3,7 4,6 5,8 7,9 Compute . Compute . What is the equation of the regression line?The number of initial public offerings of stock issued in a 10-year period and the total proceeds of these offerings (in millions) are shown in the table. Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 646. The equation of the regression line is y=32.824x+17,659.242. Issues, x 418 475 683 477 492 379 59 51 196 154 Proceeds, y 17,703 28,601 43,966 31,686 36,833 36,916 21,908 10,311 31,407 28,337 Construct and interpret a 95% prediction interval for the proceeds when the number of issues is 646. Select the correct choice below and fill in the answer boxes to complete your choice. (Round to the nearest million dollars as needed. Type your answer in standard form where "3.12 million" means 3,120,000.) A. We can be 95% confident that when there are 646 issues, the proceeds will be between $____ and $____. B. There is a 95% chance…