2.3.2: Exercise M.3

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(1) In the chart below you will find the statistics from 2003-2023 for the number of babies born, per 10,000 live births, with Down syndrome. Over those 20 years, you can see that there has been an increase.

Year	Down Syndrome at Birth per 10,000 Live Births
2003	9.5
2008	10.3
2013	10.8
2018	11
2023	11.8

(a) Using a spreadsheet application, create a scatterplot of this data and find a trendline which approximates the data in the form y = mx + b, where x is the number of years since 2003 and y is the number of Down syndrome births per 10,000 live births. Hint: Make sure you label 2003 as year 0 and all other years as time since 2003. Write the trendline below.

(b) What does this model give as the 2036 rate of Down syndrome births per 10,000 live births? Round to 1 decimal place.

(c) Do you think your linear model accurately represents the growth in babies born with Down syndrome until 2036? Explain.

(2) The data in the chart below is for the distance (in cm) to the near point, the point nearest the eye at which the eye can accurately focus, at a person’s age. Use a spreadsheet application to create a linear regression model for the data in the form y = mx + b, where x is age and y is near point. Using your model, predict the near point of someone who is 80 years old. Round your answer to 1 decimal place.

Age (years)	Near Point (cm)
10	7.5
20	9
30	11.5
40	17.2
50	52.5
60	83.3

(3) Every year, the Mauna Loa Observatory in Hawaii measures the levels of carbon dioxide (CO2) in the atmosphere. Below are the annual mean amounts, in parts per million, for the years 2006–2022:²⁰

Year	Annual mean CO2 (in ppm)
2006	382.09
2007	384.02
2008	385.83
2009	387.64
2010	390.1
2011	391.85
2012	394.06
2013	396.74
2014	398.81
2015	401.01
2016	404.41
2017	406.76
2018	408.72
2019	411.66
2020	414.24
2021	416.45
2022	418.56

(a) Create a scatterplot of the data using a spreadsheet application, then add a trendline (linear regression model) using the spreadsheet. Write the trendline in the form y = mx + b, where x is the number of years after 2006, and y is the annual mean CO2. Round your slope to 2 decimal places and your vertical intercept to the nearest whole number. (Hint: Since x is the number of years after 2006, adjust the data when you enter it in the spreadsheet.)

(b) What are the units for the input? What are the units for the output?

(d) Using your model, predict how much CO2 there will be in the atmosphere at Mauna Loa in 2050. Round to the nearest whole ppm.

(4) The graph below shows the number of smartphone users in the U.S. (in millions) from 2010 to 2021.²¹ (Note: Values for 2016–2021 were only projections.)

$Graph showing the number of smartphone users in the U.S. (in millions) from 2010 to 2021. Y-axis represents the smartphone users in millions, ranging from 0 to 36,000. X-axis represents the year, ranging from 2010 to 2021. 2010 = 62.6 2011 = 92.8 2012 = 122 2013 = 144.5 2014 = 171 2015 = 189 2016 = 207.1 2017 = 222.9 2018 = 236.3 2019 = 247.5 2020 = 256.7 2021 = 264.3$

(a) Write the linear model for the data, in the form y = mx + b, where x is the number of years since 2010 and y is the number of smartphone users, in millions.

(b) Describe any issues (or problems) with these data that might significantly affect the model’s reliability.

(5) The graph below displays the monthly sales data for a specific clothing item from 2013–2023 in the U.S. (where x is months after January 2013, and y is the number of units sold (in thousands). What trends can you identify in the sales?

$Graph showing the sales. Y-axis represents the amount of milk sold in millions of pounds, ranging from 0 to 160. X-axis represents the months after January 2013, ranging from 0 to 144. Data is shown starting in between 0 and 80 at 0 months, increasing to in between 120 and 140. Data is then shown decreasing to in between 40 and 60 at 84 months, slightly increasing to in between 60 and 80 at 132 months.$

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²⁰ http://www.esrl.noaa.gov/gmd/ccgg/trends/mlo.html

²¹ https://www.statista.com/statistics/201182/forecast-of-smartphone-users-in-the-us/

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