i 1 4 Xi 4 1 3 4 yi 16 12 17 13 22 Assume that first-order regression techniques is applicable. Use matrix methods to find: Use the same data set from problem #1. a. Obtain the residuals, e. What is the sum of the residuals? b. Obtain the residuals squared, e?. What is the sum of the squared 3. 3. 2. LO 2.
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- The following fictitious table shows kryptonite price, in dollar per gram, t years after 2006. t= Years since 2006 0 1 2 3 4 5 6 7 8 9 10 K= Price 56 51 50 55 58 52 45 43 44 48 51 Make a quartic model of these data. Round the regression parameters to two decimal places.The marketing manager of a supermarket chain would like to determine the effect of shelf spaceon the sales of pet food. A random sample of 10 stores was selected, and the results are presentedbelow. Store shelf space in cm weekly sales in thousand pesos 1 45 18 2 45 21 3 75 15 4 80 18 5 95 23 6 100 26 7 135 22 8 140 27 9 185 25 10 190 28 d. Using the estimated simple linear regression equation Y=15.6414+0.0611X, estimate the weekly sales when theshelf space is 230cm? 250cm? e. Compute the coefficient of determination and interpret its value.2. 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 (pic) a. construct a scatter plot. b. assuming a linear relationship, use the least-squares method to determine the regression coefficients b0 and b1.
- 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 ˆy=b0+b1x1+b2x2y^=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. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Adrian Beltre 104 32 18.000 Justin Smoak 34 14 3.900 Jean Segura 64 20 2.600 Justin Upton 87 31 22.125 Brandon Crawford 84 12 6.000 Curtis Granderson 59 30 16.000 Aaron Hill 38 10 12.000 Miquel Cabrera 108 38 28.050 Adrian Gonzalez 90 18 21.857 Jacoby Ellsbury 56 9 21.143 Mark Teixeira 44 15 23.125 Albert Pujols 119 31 25.000 Matt Wieters 66 17 15.800 Logan…We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=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. RBI's HR's Salary (in millions) 108 38 28.050 86 31 27.500 59 25 25.000 119 31 25.000 103 39 24.050 44 15 23.125 49 11 23.000 111 30 22.750 87 31 22.125 90 18 21.857 49 7 21.667 70 21 21.571 108 35 21.500 56 9 21.143 84 38 21.119 80 14 20.802 17 7 20.000 79 24 20.000 91 31 20.000 97 29 20.000 57 13 18.500 44 8 18.000 104 32 18.000 86 27 18.000 100 25 17.454 62 20 17.000 58 20 17.000 100 29 16.083 127 38 16.000 83 29 16.000 59 30 16.000 54…We wish to predict the salary for baseball players (yy) using the variables RBI (x1x1) and HR (x2x2), then we use a regression equation of the form ˆy=b0+b1x1+b2x2y^=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. The following is a chart of baseball players' salaries and statistics from 2016. Player Name RBI's HR's Salary (in millions) Miquel Cabrera 108 38 28.050 Yoenis Cespedes 86 31 27.500 Ryan Howard 59 25 25.000 Albert Pujols 119 31 25.000 Robinson Cano 103 39 24.050 Mark Teixeira 44 15 23.125 Joe Mauer 49 11 23.000 Hanley Ramirez 111 30 22.750 Justin Upton 87 31 22.125 Adrian Gonzalez 90 18 21.857 Jason Heyward 49 7 21.667 Jayson Werth 70 21 21.571 Matt Kemp 108 35 21.500…
- A sixth-grade teacher believes that there is a relationship between his students’ IQscores (y) and the numbers of hours (x) they spend watching television each week. Thefollowing table shows a random sample of 7 sixth-grade students.y 125 116 97 114 85 107 105x 5 10 30 16 41 28 21 Does the data provide sufficient evidence to indicate that the simple linear regressionmodel is appropriate to describe the relationship between x and y? Perform a model utilitytest at α = 0.05. (Give H0, Ha, rejection region, observed test statistic, P-value, decisionand conclusion.)Find the Pearson sample correlation coefficient between x and y. Then interpretthe result.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…Compute the least-squares regression equation for the given data set. Round the slope and y-intercept to at least four decimal places. 2 4 7 6 6 5 3 3 4 2
- The estimated regression equation for a model involvingtwo independent variables and 55 observations is: y-hat = 55.17 + 1.1X1 - 0.153X2 Other statistics produced for analysis include: SSR = 12370.8 SST = 35963.0 Sb1 = 0.33 Sb2 = 0.20 a) Interpret b1 and b2 in this estimated regression equation b. Predict y when X1 = 55 and X2 = 70. b) Compute R-square and Adjusted R-Square. e. Compute MSR and MSE. f. Compute F and use it to test whether the overall model is significant using a p-value (α = 0.05). g. Perform a t test using the critical value approach for thesignificance of β1. Use a level of significance of 0.05. h. Perform a t test using the critical value approach for thesignificance of β2. Use a level of significance of 0.05.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…The table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 13 12 11 10 9 a. 15 b. 8 c. 7 d. 20