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Mathematical Statistics with Applications
- Does Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forwardWe 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…arrow_forwardWhat is the equation for a simple linear regression model that predicts the dependent variable Y based on a single independent variable X?arrow_forward
- 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…arrow_forwardConstruct the equation of the regression line. An editing firm compiled the following table which lists the number of pages contained in a piece of technical writing and the cost of proofreading and correcting them (in dollars). Assume there is a significant linear relationship between X and Y and construct the equation of the linear regression line. Number of Pages, x 7 12 4 14 25 30 Cost, y 128 213 75 250 446 540 a.) y^= 17.9(x) + 1.6 b.) y^= 7.1(x) + 15.4 c.) y^= 15.4(x) + 7.1 d.) y^= 1.6(x) +arrow_forwardA researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆy=5−2xy^=5-2x where x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies tends to increase by 2. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 2. When amount of schooling increases by one year, the number of pregnancies tends to decrease by 5. When amount of schooling increases by one year, the number of pregnancies tends to increase by 5. . please chose one of 4 above correct answerarrow_forward
- In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least‑squares regression line was ?̂ =10+0.9?,y^=10+0.9x, where ?y represents the final exam score and ?x is the midterm exam score. Suppose Joe scores an 80 on the midterm exam. What would be the predicted value of his score on the final exam?arrow_forwardwhen the regression line passes through the origin thenarrow_forwardResearchers record the fuel consumption of a car y (in miles per gallon) at various speeds x (in miles per hour). Using software, they determine that the least-squares regression line of their data is y^=70.243−0.329x Use this to predict the fuel consumption of the car when it is moving at 20 miles per hour.arrow_forward
- The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.arrow_forwardGroundwater is the main source of water in many countries. In a study of the quality of ground water in Yemen, the authors of the paper "Multiple Linear Regression Model for Chloride Estimation of Groundwater in Ash-Shihr Town and Its Outskirts Hadharamout-Yemen"t used a multiple regression model with two independent variables, where y = chloride concentration (mg/L) X1 = total alkalinity X2 = electrical conductivity. The model equation suggested in the paper is y = -183.560 + 1.589x, + 0.069x, + e. (a) Based on this model, what is the mean value of y (in mg/L) when x, = 320 and x, = 2,700? mg/L (b) Based on this model, what mean chloride concentration (in mg/L) is associated with a total alkalinity of 270 and an electrical conductivity of 2,900? mg/Larrow_forwardA researcher wishes to examine the relationship between years of schooling completed and the number of pregnancies in young women. Her research discovers a linear relationship, and the least squares line is: ˆy=3−5xy^=3-5xwhere x is the number of years of schooling completed and y is the number of pregnancies. The slope of the regression line can be interpreted in the following way: When amount of schooling increases by one year, the number of pregnancies decreases by 3. When amount of schooling increases by one year, the number of pregnancies increases by 3. When amount of schooling increases by one year, the number of pregnancies decreases by 5. When amount of schooling increases by one year, the number of pregnancies increases by 5.arrow_forward
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