# 4.3 Fitting linear models to data  (Page 8/14)

 Page 8 / 14

Find the linear function y , where y depends on $\text{\hspace{0.17em}}x,$ the number of years since 1980.

$y=-\text{3}00x+\text{11},\text{5}00$

Find and interpret the y -intercept.

For the following exercise, consider this scenario: In 2004, a school population was 1,700. By 2012 the population had grown to 2,500.

Assume the population is changing linearly.

1. How much did the population grow between the year 2004 and 2012?
2. What is the average population growth per year?
3. Find an equation for the population, P , of the school t years after 2004.

a) 800 b) 100 students per year c) $\text{\hspace{0.17em}}P\left(t\right)=\text{1}00t+\text{17}00$

For the following exercises, consider this scenario: In 2000, the moose population in a park was measured to be 6,500. By 2010, the population was measured to be 12,500. Assume the population continues to change linearly.

Find a formula for the moose population, $\text{\hspace{0.17em}}P.$

What does your model predict the moose population to be in 2020?

18,500

For the following exercises, consider this scenario: The median home values in subdivisions Pima Central and East Valley (adjusted for inflation) are shown in [link] . Assume that the house values are changing linearly.

Year Pima Central East Valley
1970 32,000 120,250
2010 85,000 150,000

In which subdivision have home values increased at a higher rate?

If these trends were to continue, what would be the median home value in Pima Central in 2015?

\$91,625

## Fitting Linear Models to Data

Draw a scatter plot for the data in [link] . Then determine whether the data appears to be linearly related.

 0 2 4 6 8 10 –105 –50 1 55 105 160

Draw a scatter plot for the data in [link] . If we wanted to know when the population would reach 15,000, would the answer involve interpolation or extrapolation?

Year Population
1990 5,600
1995 5,950
2000 6,300
2005 6,600
2010 6,900

Extrapolation

Eight students were asked to estimate their score on a 10-point quiz. Their estimated and actual scores are given in [link] . Plot the points, then sketch a line that fits the data.

Predicted Actual
6 6
7 7
7 8
8 8
7 9
9 10
10 10
10 9

Draw a best-fit line for the plotted data.

For the following exercises, consider the data in [link] , which shows the percent of unemployed in a city of people 25 years or older who are college graduates is given below, by year.

 Year 2000 2002 2005 2007 2010 Percent Graduates 6.5 7 7.4 8.2 9

Determine whether the trend appears to be linear. If so, and assuming the trend continues, find a linear regression model to predict the percent of unemployed in a given year to three decimal places.

In what year will the percentage exceed 12%?

2023

Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.

 $x$ 17 20 23 26 29 $y$ 15 25 31 37 40

Based on the set of data given in [link] , calculate the regression line using a calculator or other technology tool, and determine the correlation coefficient to three decimal places.

 $x$ 10 12 15 18 20 $y$ 36 34 30 28 22

For the following exercises, consider this scenario: The population of a city increased steadily over a ten-year span. The following ordered pairs show the population and the year over the ten-year span (population, year) for specific recorded years:

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