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#### Description:

Created by Illuminations: Resources for Teaching Mathematics, this unit plan contains nine lessons about interpreting the slope and y-intercept of least squares regression lines in the context of real-life data. The applet included allows students to plot the data and calculate the correlation coefficient and the equation of the regression line. Students will view the data in tabular, graphic, and algebraic form and will be able to discuss and display their work. This is a wonderful collection of interactive statistical lessons. They can easily be translated into classroom activities.

#### Subjects:

• Mathematics > General

#### Keywords:

Vocational/Professional Development Education,statistics,NSDL,mathematical tools,regression analysis,graph,Undergraduate (Lower Division),NSDL_SetSpec_ncs-NSDL-COLLECTION-000-003-112-016,Physics,motion in one dimension,Higher Education,High School,graphing,Technology,graphical analysis,Mathematics,mathematics,linear regression,physics,classical mechanics,oai:nsdl.org:2200/20120614151545395T

English

#### Access Privileges:

Public - Available to anyone

Creative Commons Attribution Non-Commercial Share Alike

#### Collections:

None
Update Standards?

#### CCSS.Math.Content.HSS-ID.A.1: Common Core State Standards for Mathematics

Represent data with plots on the real number line (dot plots, histograms, and box plots).

#### CCSS.Math.Content.HSS-ID.A.2: Common Core State Standards for Mathematics

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

#### CCSS.Math.Content.HSS-ID.A.3: Common Core State Standards for Mathematics

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

#### CCSS.Math.Content.HSS-ID.A.4: Common Core State Standards for Mathematics

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

#### CCSS.Math.Content.HSS-ID.B.6a: Common Core State Standards for Mathematics

Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

#### CCSS.Math.Content.HSS-ID.B.6b: Common Core State Standards for Mathematics

Informally assess the fit of a function by plotting and analyzing residuals.

#### CCSS.Math.Content.HSS-ID.B.6c: Common Core State Standards for Mathematics

Fit a linear function for a scatter plot that suggests a linear association.

#### CCSS.Math.Content.HSS-ID.C.7: Common Core State Standards for Mathematics

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

#### CCSS.Math.Content.HSS-ID.C.8: Common Core State Standards for Mathematics

Compute (using technology) and interpret the correlation coefficient of a linear fit.

#### CCSS.Math.Content.HSS-ID.C.9: Common Core State Standards for Mathematics

Distinguish between correlation and causation.

#### CCSS.Math.Content.HSS-IC.A.1: Common Core State Standards for Mathematics

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

#### CCSS.Math.Content.HSS-IC.B.3: Common Core State Standards for Mathematics

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

#### CCSS.Math.Content.HSS-IC.B.4: Common Core State Standards for Mathematics

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

#### CCSS.Math.Content.HSS-IC.B.5: Common Core State Standards for Mathematics

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

#### CCSS.Math.Content.HSS-IC.B.6: Common Core State Standards for Mathematics

Evaluate reports based on data.

#### CCSS.Math.Content.HSS-MD.A.1: Common Core State Standards for Mathematics

(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

#### CCSS.Math.Content.HSS-MD.A.2: Common Core State Standards for Mathematics

(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

#### CCSS.Math.Content.HSS-MD.A.3: Common Core State Standards for Mathematics

(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

#### CCSS.Math.Content.HSS-MD.A.4: Common Core State Standards for Mathematics

(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

#### CCSS.Math.Content.HSS-MD.B.6: Common Core State Standards for Mathematics

(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

#### CCSS.Math.Content.HSS-MD.B.7: Common Core State Standards for Mathematics

(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
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