Consider the following data points.P₁(1, 8), P₂(2, 6), Ps(5, 6), P4(6, 5), Ps(10, 1)(a) Find the equation of the least-squares line for the data. (Round all coefficients to two decimal places.)y(b) Draw a scatter diagram for the data and graph the least-squares line.y862628810102422881010x

The equation of the straight line, obtained using least squares method, is y=8.4882−0.685x.

Answered: Consider the following data points.…

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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A scientist collected data on the mating call frequency of frogs and temperature. They found the least squares line to be: y = 3 + 5x where x is the temperature (in Celsius) and y is mating call frequency. The slope of the regression line can be interpreted in the following way: OWhen temperature decreases by one degree, the mating call frequency increases by 5. When temperature increases by one degree, the mating call frequency increases by 3. O When temperature increases by one degree, the mating call frequency increases by 5. O When temperature decreases by one degree, the mating call frequency increases by 3. OWhen temperature increases by one degree, the mating call frequency decreases by 5. Submit Question
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An issue of USA Today reported the average fees charged to use another bank's ATM for 2000-2005. Year ATM Fee 2000 $2.65 2001 $2.54 2002 $2.76 2003 $2.87 2004 $2.69 2005 $2.93 (a) Use these data to find a least squares line of ATM fees as a function of years since 2000. (Round your coefficients to three decimal places.)y = (b) Estimate the average ATM fee for 2019. (Round your answer to the nearest cent.)
(d) What percentage of the variation in diastolic blood pressure can be explained by systolic blood pressure? (e) Find an equation of the least-squares regression line for systolic blood pressure and diastolic blood pressure. A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures taken at rest were measured, in millimeters, for a sample of 15 adults. The following table presents the results. 130 116 133 112 107 110 105 157 154 Systolic Diastolic 134 115 113 123 119 118 87 83 77 77 69 88 76 70 91 75 71 74 66 103 94 Below is a scatterplot of the data set.
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Mass-Transit Subsidies The following table gives the projected state subsidies (in millions of dollars) to a certain transit authority over a 5-year period (x = 1 corresponds to the first year). Year, x 3 4 Subsidy, y 21.25 25.5 24.25 26.25 33.75 (a) Find an equation of the least-squares line for these data. y = (b) Assuming that the trend continued, estimate the state subsidy to the MBTA (in millions of dollars) for the eighth year (x 8). (Round your answer to one decimal place.) %24 million
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We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state.A Minitab printout provides the following information.Predictor Coef SE Coef T PConstant 317.70 28.31 11.22 0.0015Elevation −31.8123.511 −9.060.0028s = 11.8603, R-Sq = 96.5%Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx.(a)Use the printout to write the least-squares equation.ŷ = (b)For each 1,000-foot increase in elevation, how many…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 315.27 28.31 11.24 0.002 Elevation -31.353 3.511 -8.79 0.003 S = 11.8603 R-Sq = 96.0% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation, how…
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) through (d) below. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=nothingx+(nothing) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on…
We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squares equation is not given directly. Instead, the value of the constant a is given, and the coefficient b of the explanatory or predictor variable is displayed. Sometimes a is referred to as the constant, and sometimes as the intercept. Data from a report showed the following relationship between elevation (in thousands of feet) and average number of frost-free days per year in a state. A Minitab printout provides the following information. Predictor Coef SE Coef T P Constant 318.24 28.31 11.24 0.002 Elevation -30.759 3.511 -8.79 0.003 S = 11.8603 R-Sq = 97.2% Notice that "Elevation" is listed under "Predictor." This means that elevation is the explanatory variable x. Its coefficient is the slope b. "Constant" refers to a in the equation ŷ = a + bx. (a) Use the printout to write the least-squares equation. ŷ = + x (b) For each 1000-foot increase in elevation,…

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Consider the following data points. P₁(1, 8), P₂(2, 6), P3(5, 6), P4(6, 5), Pg(10, 1) (a) Find the equation of the least-squares line for the data. (Round all coefficients to two decimal places.) y- (b) Draw a scatter diagram for the data and graph the least-squares line.