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compare to the actual data points on the graph? Which model do you think fits the data best and why?

compare to the actual data points on the graph? Which model do you think fits the data best and why?

Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
8th Edition
ISBN:9781337091992
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter17: Production And Growth
Section: Chapter Questions
Problem 8PA
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1. You have been hired as a consultant for the City of Los Angeles. City planners need to understand population data and use the data to predict the population in the future. Having a good estimate of the city's population helps the planners decide how much money will be needed for city maintenance and services, and helps local officials anticipate the needs for housing, school and other construction, and much more. Your work begins with finding the population of Los Angeles in the United States Census for 1920 to 2010. The U.S. Census Bureau data for the City of Los Angeles 1920-2010 appears in table below. Year Actual Population using Population using Quadratic Model Population using Exponential Model х, уears since Population Linear Model 1920 1920 576,673 10 1930 1,238,048 20 1940 1,504,277 30 1950 1,970,358 40 1960 2,479,015 50 1970 2,816,061 60 1980 2,966,850 70 1990 3,485,398 80 2000 3,694,820 90 2010 3,792,621 a. One way to model the population is with a linear function, y = mx + b, where x is the years since 1920 and y is the population. As a first attempt, find a linear model for the population using just the data for 1920, (0, 576673), and 2010, (90,3792621). Show all work algebraically and round all values to two decimal places. b. Enter the values for x and the actual population as a table in Desmos and use regression to find the best linear function that models the data by entering y,~mx, + b. Give this model below (rounding all values to two decimal places) and use it to fill in the column labeled "Population using Linear Model" in the table above. c. How do your models from parts (a) and (b) compare? How do each of the two models compare to the actual data points on the graph? Which model do you think fits the data best and why?
Transcribed Image Text:1. You have been hired as a consultant for the City of Los Angeles. City planners need to understand population data and use the data to predict the population in the future. Having a good estimate of the city's population helps the planners decide how much money will be needed for city maintenance and services, and helps local officials anticipate the needs for housing, school and other construction, and much more. Your work begins with finding the population of Los Angeles in the United States Census for 1920 to 2010. The U.S. Census Bureau data for the City of Los Angeles 1920-2010 appears in table below. Year Actual Population using Population using Quadratic Model Population using Exponential Model х, уears since Population Linear Model 1920 1920 576,673 10 1930 1,238,048 20 1940 1,504,277 30 1950 1,970,358 40 1960 2,479,015 50 1970 2,816,061 60 1980 2,966,850 70 1990 3,485,398 80 2000 3,694,820 90 2010 3,792,621 a. One way to model the population is with a linear function, y = mx + b, where x is the years since 1920 and y is the population. As a first attempt, find a linear model for the population using just the data for 1920, (0, 576673), and 2010, (90,3792621). Show all work algebraically and round all values to two decimal places. b. Enter the values for x and the actual population as a table in Desmos and use regression to find the best linear function that models the data by entering y,~mx, + b. Give this model below (rounding all values to two decimal places) and use it to fill in the column labeled "Population using Linear Model" in the table above. c. How do your models from parts (a) and (b) compare? How do each of the two models compare to the actual data points on the graph? Which model do you think fits the data best and why?
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