Topics
9. Data Analysis
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United States of AmericaVirginia
Algebra 1

9.03 Linear regression

Lesson
Practice
Adaptive
Worksheet

Interactive practice questions

The scatter diagram shows the number of restaurants in a city over time.

Loading Graph...
A scatter plot is depicted with a vertical y-axis and a horizontal x-axis, both unlabeled except for the notations 'y' and 'x' at their respective ends. There are seven distinct black dots scattered across the plot, with coordinates at $\left(1,\frac{11}{20}\right)$(1,1120​), $\left(2,\frac{27}{20}\right)$(2,2720​), $\left(3,\frac{53}{20}\right)$(3,5320​), $\left(4,\frac{69}{20}\right)$(4,6920​), $\left(5,\frac{17}{4}\right)$(5,174​), $\left(6,\frac{101}{20}\right)$(6,10120​), and $\left(7,\frac{107}{20}\right)$(7,10720​). The dots form a not-so-perfect straight line if they are connected. The graph indicates that as time increases, the number of parks in a city also increases. The coordinates of the points are not explicitly shown in the image.
a

Which type of model would be appropriate for this data?

Linear

A

Quadratic

B
b

Will the slope of the line in the linear model be positive or negative?

Positive

A

Negative

B
Easy
< 1min

The scatter diagram shows the number of sales of hot-chocolate a cafe makes as a function of temperature.

Easy
< 1min

Which of the following could be the equation for the line of best fit?

Medium
< 1min

Consider the scatter plot.

Medium
1min
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Outcomes

A.ST.1

The student will apply the data cycle (formulate questions; collect or acquire data; organize and represent data; and analyze data and communicate results) with a focus on representing bivariate data in scatterplots and determining the curve of best fit using linear and quadratic functions.

A.ST.1a

Formulate investigative questions that require the collection or acquisition of bivariate data.

A.ST.1b

Determine what variables could be used to explain a given contextual problem or situation or answer investigative questions.

A.ST.1c

Determine an appropriate method to collect a representative sample, which could include a simple random sample, to answer an investigative question.

A.ST.1d

Given a table of ordered pairs or a scatter plot representing no more than 30 data points, use available technology to determine whether a linear or quadratic function would represent the relationship, and if so, determine the equation of the curve of best fit.

A.ST.1e

Use linear and quadratic regression methods available through technology to write a linear or quadratic function that represents the data where appropriate and describe the strengths and weaknesses of the model.

A.ST.1f

Use a linear model to predict outcomes and evaluate the strength and validity of these predictions, including through the use of technology.

A.ST.1g

Investigate and explain the meaning of the rate of change (slope) and y-intercept (constant term) of a linear model in context.

A.ST.1h

Analyze relationships between two quantitative variables revealed in a scatterplot.

A.ST.1i

Make conclusions based on the analysis of a set of bivariate data and communicate the results.

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