11-1/435(a) Calculate the least squares estimates of the slope andintercept. Graph the regression line.(b) Use the equation of the fitted line to predict whatbody fat would be observed, on average, for a manwith a BMI of 30.(c) Suppose that the observed body fat of a man with aBMI of 25 is 25%. Find the residual for thatobservation.(d) Was the prediction for the BMI of 25 in part (c) anoverestimate or underestimate? Explain briefly. 11-1/435 Diabetes and obesity are serious healthconcerns in the United States and much of thedeveloped world. Measuring the amount of body fat aperson carries is one way to monitor weight controlprogress, but measuring it accurately involves eitherexpensive X-ray equipment or a pool in which to dunkthe subject. Instead body mass index (BMI) is oftenused as a proxy for body fat because it is easy tomeasure: BMI = mass (kg)/(height (m))2 = 703mass(Ib)/(height (in))2. In a study of 250 men atBingham Young University, both BMI and body fat weremeasured. Researchers found the following summarystatistics:11-1/4352 xi = 6322.28x = 162674.18Yi = 4757.90> yi = 107679.27X¡Yi = 125471.10i=1

Answered: Image /qna-images/answer/7a2a82ba-39a0-4c67-90d7-0cb7022cddd8.jpg

Answered: (a) Calculate the least squares…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The object in linear regression is to obtain an equation of a curve that minimizes the sum of squared vertical deviations of data points from the line. true or false?
A trucking company considered a multiple regression model for relating the dependent variable y = total daily travel time for one of its drivers (hours) to the predictors x₁ = distance traveled (miles) and x₂ = the number of deliveries made. Suppose that the model equation is Y = -0.800+ 0.060x₁ +0.900x₂ + e (a) What is the mean value of travel time when distance traveled is 50 miles and four deliveries are made? hr (b) How would you interpret ₁ = 0.060, the coefficient of the predictor x₁? O When the number of deliveries is constant, the average change in travel time associated with a ten-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The total daily travel time increases by 0.060 hours when the distance traveled increases by 1. O When the number of deliveries is held fixed, the average change in travel time associated with a one-mile (i.e. one unit) increase in distance traveled is 0.060 hours. O The average change in travel time associated with a one-mile (i.e.…
The owner of a movie theater company used multiple regression analysis to predict gross revenue (y) as a function of television advertising (x,) and newspaper advertising (x,). The estimated regression equation was ý = 82.3 + 2.29x, + 1.90x2. The computer solution, based on a sample of eight weeks, provided SST = 25.1 and SSR = 23.415. (a) Compute and interpret R? and R 2. (Round your answers to three decimal places.) The proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is 653 x . Adjusting for the number of independent variables in the model, the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation is (b) When television advertising was the only independent variable, R2 = 0.653 and R,2 = 0.595. Do you prefer the multiple regression results? Explain. Multiple regression analysis (is preferred since both R2 and R.2 show an increased v v…
A set of n=15 pairs of x and y scores has sx=10, ssy=40, and sp=30. What is the slope for the regression for predicting y from x?
A least squares regression line was calculated to relate the length (cm) of newborn boys to their weight in kg. The line is weight = -5.25 +0.1696 length. A newborn was 48 cm long and weighed 3 kg. According to the regression model, what was his residual? What does that say about him?
A biologist is interested in predicting the percentage increase in lung volume when inhaling (y) for a certain species of bird from the percentage of carbon dioxide in the atmosphere (x). Data collected from a random sample of 20 birds of this species were used to create the least-squares regression equation ŷ = 400-0.08x. Which of the following best describes the meaning of the slope of the least-squares regression line? (A) The percentage increase in lung volume when inhaling increases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (B) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on average, for every 1 percent increase in lung volume when inhaling. (C) The percentage increase in lung volume when inhaling decreases by 0.08 percent, on average, for every 1 percent increase in the carbon dioxide in the atmosphere. (D) The percentage of carbon dioxide in the atmosphere increases by 0.08 percent, on…
The distance between the Y value in the data and the predicted Y value from the regression equation is known as the residual. What is the value for the sum of the squared residuals? a. SSresidual = r2(SSX) b. SSresidual = r2(SSY) c. SSresidual = (1 – r2)(SSX) d. SSresidual = (1 – r2)(SSY)
The trip rate (y) and the corresponding household sizes (x) from a sample are shown in Table Q2. Apply the regression method to find the trip rate for a household size of 10. Table Q2
The police chief believes that maintenance costs on high-mileage police vehicles are much higher than those costs for low-mileage vehicles. If high-mileage vehicles are costing too much, it may be more economical to purchase more vehicles. An analyst in the department regresses yearly maintenance costs (Y) for a sample of 200 police vehicles on each vehicle’s total mileage for the year (X). The regression equation finds: Y = $50 + .030X with a r2 of .90 If a vehicle’s mileage for the year is 50,000, what is its predicted maintenance costs? What does an r2 of .90 tell us? Is this a strong or weak correlation? How can you tell?
B b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates a positive linear relationship between a = average number of passing yar and y = the percentage of games won by the team. c. Develop the estimated regression equation that could be used to predict the percentage of games won given the avera passing yards per attempt. Enter negative value as negative number. WinPct =| |)(Yds/Att) (to 4 decimals) d. Provide an interpretation for the slope of the estimated regression equation (to 1 decimal). The slope of the estimated regression line is approximately So, for every increase : of one yar number of passes per attempt, the percentage of games won by the team increases by %. e. For the 2011 season, the average number of passing yards per attempt for the Kansas City Chiefs was was 5.5. Use th regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs.…
In calculating a simple regression for average number of drinks consumed (x) and grade point average (y), you get a slope coefficient (b) of -.15 and a y intercept of 2.50. Using the formula Y = a + bX, what would the predicted grade point average be for a student who averaged 1.0 drinks per week?
8. Which is the linear regression equation for a scatterplot with these points rounded to the nearest tenth: (4, 35), (6.5, 92), (2. 10). (5, 50), (6, 85), (10, 110)?

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