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Regression Lines

LEARN
EXPLORE

Concept:

Using the elementary functions of mathematics with data collected from experimentation or from polling can be facilitated by least-squares curve fitting.

n =

residual

y = ax + b

y = ax² + bx + c

y = ae^bx

y = a + b ln x

y =

ax + b / x + c

y = ax^b

INSTRUCTIONS

Select a data set, or enter your own, and decide which functional model best represents the data by comparing residuals. Use the checkboxes to select which curves to display, or whether to display the data. Basic editing can be done on the data by means of the editing buttons or by using common editing controls. You can use up to 100 points of your own data in the form of a comma-separated list of ordered pairs. The quality of the fit of different curves can be compared against each other for a given data set with the residuals. A smaller residual means a better fit.

EXPLORATIONS

Exploration 1:
What is the difference between the exponential model and the power model?

Exploration 2:
Why might a linear model rarely be the best fit for real-world data?

Exploration 3:
Experiment with Random data sets: click the Random button and try to predict which model fits the plot best before checking your guess by comparing the residuals. Do this several times, until you think you can accurately predict the model for random data in a reliable manner.

PRACTICE QUESTIONS

1 2 3 4 5 6

1. What is coefficient of x in the numerator of the rational model for the power law data set?

–84.2

–71.7

–63.9

–50.1

Correct ! Good Job!

2. What is the slope of the line for the exponential data set?

–2.56

–0.77

1.224

5.896

Correct ! Good Job!

3. What is the value of the exponent for the power law model for the rational data set?

–0.37

–0.22

0.38

0.74

Correct ! Good Job!

4. Which type of function has the smallest residual for the linear data set?

linear

quadratic

logarithmic

rational

Correct ! Good Job!

5. What is the value of the multiplier a of the exponential model for the logarithmic data set?

8.84

25.4

26.5

73.5

Correct ! Good Job!

6. What is the value of the constant c for the quadratic model in the quadratic data set?

15.3

29.3

35.4

45.1

Correct ! Good Job!

n be any number from to

$t$ can be any number from to