A certain experiment produces the data (1, 1.6), (2, 2.9), (3, 3.3), (4, 3.8), and (5, 3.9). Describe the model that produces a least-squares fit of these pts by a function of the form y = β1 x + β2x2. Such a function might arise, for exmple, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price to be set for the product.

A certain experiment produces the data (1, 1.6), (2, 2.9), (3, 3.3), (4, 3.8), and (5, 3.9). Describe the model that produces a least-squares fit of these pts by a function of the form y = β1 x + β2x2. Such a function might arise, for exmple, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price to be set for the product.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
An airline developed a regression model to predict revenue from flights that connect "feeder" cities to its hub airport. The response in the model is the revenue generated by flights operating to the feeder cities (in thousands of dollars per month), and the two explanatory variables are the air distance between the hub and feeder city (Distance, in miles) and the population of the feeder city (in thousands). The least squares regression equation based on data for 37 feeder locations last month is Estimated revenue = 81 +0.3Distance + 1.4Population with R² = 0.75 and so = 31.2. Complete parts a through d. (a) The airline plans to expand its operations to add an additional feeder city. The first possible city has population 150,000 and is 275 miles from the hub. A second possible city has population 180,000 and is 250 miles from the hub. Which would you recommend if the airline wants to increase total revenue? The first city The second city
FRQ 2 Professional basketball teams have 11 players per team. Salary is dependent upon their scoring average, measured in points per game. A least-squares regression line that describes the relationship between scoring average and salary for one professional basketball team is ŷ = 2,671,134.68 +684,663.08x, where x is the player's scoring average and y is the player's salary. The residuals for this regression are given in the graph below. Residual $20,000,000 $15,000,000 $10,000,000 $5,000,000 $0 -$5,000,000 -$10,000,000 -$15,000,000 4 ITS % 6 MacBook Pro ● 8 ● ● ● 10 12 14 Scoring Average (Points per Game) Is a line an appropriate model to use for these data? What information tells you this? b) What is the value of the slope of the least-squares regression line? Interpret the slope in the context of this problem. c) What is the predicted salary of the basketball player with 10.9 points per game? d) Approximate the actual salary of the basketball player with 10.9 points per game. 16 tv…
The following gives the number of accidents that occurred on Florida State Highway 101 during the last 4 months: Month Number of Accidents Jan 25 Feb 40 Mar 60 Apr 90 Using the least-squares regression method, the trend equation for forecasting is (round your responses to two decimal places): ŷ-0-0x Using least-squares regression, the forecast for the number of accidents that will occur in the month of May = accidents (enter your response as a whole number).
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable.
The following Minitab display gives information regarding the relationship between the body weight of a child (in kilograms) and the metabolic rate of the child (in 100 kcal/ 24 hr). Predictor Constant Weight S = 0.517508 Coef 0.8462 0.39512 R-Sq 97.0% (a) Write out the least-squares equation. ŷ = = 0.8462 + 0.39512 X SE Coef 0.4148 0.02978 T 2.06 13.52 P (c) What is the value of the correlation coefficient r? (Use 3 decimal places.) X 0.84 0.000 (b) For each 1 kilogram increase in weight, how much does the metabolic rate of a child increase? (Use 5 decimal places.) 0.39512
A student is preparing to take a stand allies exam she was told that she needs to get plenty of sleep the night before the exam she is interested in the relationship between the number of hours of sleep a student gets her for an exam and the score earned on the exam. She collects information from 10 other students who have already taken the exam as shown on the table. she fits at least squares regression line to the data and determines the equation of the line is why equals 26-0.18 X where why is the score earn on the exam and ask is the number of hours of sleep the night before the exam. The residual is given. based on the residual plot is the linear model appropriate? no, there is no clear pattern in the residual plot. yes, there is no clear pattern in the residual plot. no, the student who got the most you've had a negative residual yes, there are more negative residuals (6) then positive residuals (4)
A financial analyst is examinıng the Pela each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be y = -0.147+0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per Current stock price, y (in dollars) share, x (in dollars) 36.55 1.64 14.18 0.57 41.79 1.37 39.16 1.10 2.5+ 57.70 2.71 26.95 0.90 32.65 1.70 41.94 1.17 52.79 2.56 42.72 2.01 16.89 0.76 22.46 0.58 Earnings per share, x (in dollars) 58.88 2.19 30.13 1.48 50.08 1.73 28.92 0.81 Submit Assi Continue D 2021 McGraw-H Education. All Rights Reserved. Terms of Use Privacy e to search 近 Current stock price, y (in dollars)
Draw a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Then draw the least-squares regression line on the graph.
The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are displayed in the scatterplot. The equation ŷ = 17.4 + 0.5x is called the least-squares regression line because it is least able to make accurate predictions for the data. makes the strongest association between weight and height. minimizes the sum of the squared distances from the actual y-value to the predicted y-value. maximizes the sum of the squared distances from the actual y-value to the predicted y-value.
A pediatrician wants to determine the relationship that exists between achild’s height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences, and conducts the least-squares regression analysis with the simple linear model using StatCrunch. The output is given below: (a) Write down the equation of the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Use the regression equation to predict the head circumference of a child who is 25 inches tall. Assume that the regression model is applicable.(d) It is observed that one child who is 25 inches tall has a head circumference of 17.5 inches. Is the observed value above or below average among all children with heights of 25 inches?
An engineer is testing a new car model to determine how its fuel efficiency, measured in L/(100 km), is related to its speed, which is measured in km/hour. The engineer calculates the average speed for 30 trials. The average speed is an example of a (statistic or parameter) The engineer would like to find the least squares regression line predicting fuel used (y) from speed (x) for the 30 cars he observed. He collected the data below. Speed 62 65 80 82 85 87 90 96 98 100 Fuel 12 13 14 13 14 14 15 15 16 15 Speed 100 102 104 107 112 114 114 117 121 122 Fuel 16 17 16 17 18 17 18 17 18 19 Speed 124 127 127 130 132 137 138 142 144 150 Fuel 18 19 20 19 21 23 22 23 24 26 The regression line equation is Round each number to four decimal places.