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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_forwardWhat is the equation for a simple linear regression model that predicts the dependent variable Y based on a single independent variable X?arrow_forwardThe authors of the paper "Power-Load Prediction Based on Multiple Linear Regression Model"t were interested in predicting the load on the electric power system in China using data on y = Power consumption (in hundreds of millions of kwh), x, Population (in millions), and x, = Gross domestic %3D product (in billions of dollars), for 21 years. The model equation proposed in the paper is y = -113,527 + 0.974x, + 0.057x, + e. (a) According to this model, what is the mean power consumption (in hundreds of millions of kwh) for a year if the population was 160,000 million and the gross domestic product was 600,000 billion dollars? hundreds of millions of kwh (b) Interpret the value of B, in this model. When the [ gross domestic product v is fixed, the mean increase in [power consumption (in hundreds of millions of kwh) V associated with a 1-million unit increase in [population is 0.974.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_forwardIn 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_forward
- A 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_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 study was done to look at the relationship between number of movies people watch at the theater each year and the number of books that they read each year. The results of the survey are shown below. Movies 8 2 7 9 9 2 0 7 4 4 9 Books 0 8 0 0 0 4 9 0 1 0 0 The equation of the linear regression line is: ˆyy^ = + xx (Please show your answers to two decimal places) Use the model to predict the number of books read per year for someone who watches 6 movies per year.Books per year = (Please round your answer to the nearest whole number.) Interpret the slope of the regression line in the context of the question: For every additional movie that people watch each year, there tends to be an average decrease of 0.88 books read. The slope has no practical meaning since people cannot read a negative number of books. As x goes up, y goes down. Interpret the y-intercept in the context of the question: If someone watches 0 movies per year, then that person will read…arrow_forward
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