A particular professor has noticed that the number of people, P, who complain about his attitude isdependent on the number of cups of coffee, n, he drinks. From eight days of tracking he compiledthe following data:People (P)119764Cups of coffee (n)123445Unless otherwise stated, you can round values to two decimal places.a) Using regression to find a linear equation for P(n)P(n) =%3Db) Interpret the meaning of the slope of your formula in the context of the problem

a) It is considered that; the independent variable is the cups of coffee (x) and the dependent…

Answered: A particular professor has noticed that…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.3: Fitting Linear Models To Data

Problem 34SE: For the following exercises, consider this scenario: The profit of a company decreased steadily...

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Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
For the following exercises, consider this scenario: The profit of a company decreased steadily overa ten-year spam.The following ordered pairs shows dollars and the number of units sold in hundreds and the profit in thousands ofover the ten-year span, (number of units sold, profit) for specific recorded years: (46,600),(48,550),(50,505),(52,540),(54,495). Use linear regression to determine a function Pwhere the profit in thousands of dollars depends onthe number of units sold in hundreds.
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate.The slope tells us the decrease in the number of education doctorates for each additional social science doctorate. The slope tells us the increase in the number…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number of social science doctorates for each additional education doctorate. The slope tells us the increase in the number of social science doctorates for each additional education doctorate.…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Graph the associated points and regression line. (b) What does the slope tell you about the relationship between the number of social science doctorates and the number of education doctorates? The slope tells us the increase in the number of social science doctorates for each additional education doctorate.The slope tells us the increase in the number of education doctorates for each additional social science doctorate. The slope tells us the decrease in the number…
he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
Suppose a study wants to predict the market price of a certain species of turtle (Y) based on the following independent variables indicated in the table. Based from the table, what is the equation of the multiple linear regression? (Round off up to two decimal places. Market Price = 0.07 - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = - 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 + 0.40*weight + 1.51*length + 1.41*width + 0.80*age Market Price = 0.07 - 0.40 + weight + 1.51 + length + 1.41 + width + 0.80 + age
The following are data on the average weekly profits(in $1,000) of five restaurants, their seating capacities, andthe average daily traffic (in thousands of cars) that passestheir locations: Seating Traffic Weekly netcapacity count profitx1 x2 y120 19 23.8200 8 24.2150 12 22.0180 15 26.2240 16 33.5 (a) Assuming that the regression is linear, estimate β0, β1,and β2.(b) Use the results of part (a) to predict the averageweekly net profit of a restaurant with a seating capacityof 210 at a location where the daily traffic count averages14,000 cars.
The following table shows the length, in centimeters, of the humerus and the total wingspan, in centimeters, of several pterosaurs, which are extinct flying reptiles. (A graphing calculator is recommended.) (a) Find the equation of the least-squares regression line for the data. (Where × is the independent variable.) Round constants to the nearest hundredth. y= ? (b) Use the equation from part (a) to determine, to the nearest centimeter, the projected wingspan of a pterosaur if its humerus is 52 centimeters. ? cm

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