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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_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_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. 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…arrow_forward
- Construct 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_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
- when 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_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
- Groundwater 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_forwardThe 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_forwardHormone replacement therapy (HRT) is thought to increase the risk of breast cancer. The accompanying data on x = percent of women using HRT and y = breast cancer incidence (cases per 100,000 women) for a region in Germany for 5 years appeared in the paper "Decline in Breast Cancer Incidence after Decrease in Utilization of Hormone Replacement Therapy." The authors of the paper used a simple linear regression model to describe the relationship between HRT use and breast cancer incidence. † HRT Use Breast Cancer Incidence 46.30 103.30 40.60 105.00 39.50 100.00 36.60 93.80 30.00 83.50 (a) What is the equation of the estimated regression line? (Round your numerical values to four decimal places.) ŷ = (b) What is the estimated average change in breast cancer incidence (in cases per 100,000 women) associated with a 1 percentage point increase in HRT use? (Round your answer to four decimal places.) cases per 100,000 women (c) What breast cancer…arrow_forward
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