<< Chapter < Page Chapter >> Page >

Using a regression line to make predictions

Gasoline consumption in the United States has been steadily increasing. Consumption data from 1994 to 2004 is shown in [link] . http://www.bts.gov/publications/national_transportation_statistics/2005/html/table_04_10.html Determine whether the trend is linear, and if so, find a model for the data. Use the model to predict the consumption in 2008.

Year '94 '95 '96 '97 '98 '99 '00 '01 '02 '03 '04
Consumption (billions of gallons) 113 116 118 119 123 125 126 128 131 133 136

The scatter plot of the data, including the least squares regression line, is shown in [link] .

Scatter plot, showing the line of best fit. It is titled 'Gas Consumption VS Year'. The x-axis is 'Year After 1994', and the y-axis is 'Gas Consumption (billions of gallons)'. The points are strongly positively correlated and the line of best fit goes through most of the points completely.

We can introduce new input variable, t , representing years since 1994.

The least squares regression equation is:

C ( t ) = 113.318 + 2.209 t

Using technology, the correlation coefficient was calculated to be 0.9965, suggesting a very strong increasing linear trend.

Using this to predict consumption in 2008 ( t = 14 ) ,

C ( 14 ) = 113.318 + 2.209 ( 14 )           = 144.244

The model predicts 144.244 billion gallons of gasoline consumption in 2008.

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Use the model we created using technology in [link] to predict the gas consumption in 2011. Is this an interpolation or an extrapolation?

150.871 billion gallons; extrapolation

Got questions? Get instant answers now!

Access these online resources for additional instruction and practice with fitting linear models to data.

Key concepts

  • Scatter plots show the relationship between two sets of data. See [link] .
  • Scatter plots may represent linear or non-linear models.
  • The line of best fit may be estimated or calculated, using a calculator or statistical software. See [link] .
  • Interpolation can be used to predict values inside the domain and range of the data, whereas extrapolation can be used to predict values outside the domain and range of the data. See [link] .
  • The correlation coefficient, r , indicates the degree of linear relationship between data. See [link] .
  • A regression line best fits the data. See [link] .
  • The least squares regression line is found by minimizing the squares of the distances of points from a line passing through the data and may be used to make predictions regarding either of the variables. See [link] .

Section exercises


Describe what it means if there is a model breakdown when using a linear model.

When our model no longer applies, after some value in the domain, the model itself doesn’t hold.

Got questions? Get instant answers now!

What is interpolation when using a linear model?

Got questions? Get instant answers now!

What is extrapolation when using a linear model?

We predict a value outside the domain and range of the data.

Got questions? Get instant answers now!

Explain the difference between a positive and a negative correlation coefficient.

Got questions? Get instant answers now!

Explain how to interpret the absolute value of a correlation coefficient.

The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.

Got questions? Get instant answers now!


A regression was run to determine whether there is a relationship between hours of TV watched per day ( x ) and number of sit-ups a person can do ( y ) . The results of the regression are given below. Use this to predict the number of sit-ups a person who watches 11 hours of TV can do.

y = a x + b a = −1.341 b = 32.234   r = −0.896
Got questions? Get instant answers now!

Questions & Answers

what is the coefficient of -4×
Mehri Reply
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
I'm 13 and I understand it great
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
is it a question of log
I rally confuse this number And equations too I need exactly help
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
greetings from Iran
salut. from Algeria
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
Practice Key Terms 5

Get the best College algebra course in your pocket!

Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?