Algebra 2 Project : Scatter Plots and Best-Fit Lines



Scatter Plots and Best-Fit Lines Project

In this project you will perform regression analysis on data to develop a mathematical model that relates two variables. Then you will use this model to make predictions.

Step 1 – Find data that you think might be correlated. You must have at least 20 data points, but not more than 50. Here are some sample ideas to get you thinking:

• Age (months or years) and weight of people, or alligators or dogs

• Elevation of tree line compared to latitude (you would need to find this on the internet)

• Year and population of a town, city, county, country

• Year and education spending per student (national/state)

• a Major League Baseball team’s games won and total errors made (check internet)

• NBA player salary versus their free throw percentage

Step 2 – Present your data in table form, with labels. Identify which set of numbers are your x values (independent variable), and which are your y-values (dependent variable).

Step 3 – Create a scatterplot of your data. Your final draft should be on 8.5” x 11” graph paper, neatly drawn, well-labeled, with appropriate titles.

Step 4 – Construct a best-fit line for your data using mean points. Draw and label it onto the scatter plot. Find its equation, in slope-intercept form (with the slope in simplest form). All work must be shown on another piece of paper.

*Paper: explain the meaning of your line of best fit (paper detail below)

Step 5 – Construct the regression line. You may use your calculator to find the equation. Draw and label it with a different color onto the scatter plot. Find its equation, in slope-intercept form (with the slope in simplest form).

*Paper: explain the meaning of the regression line, what the correlation coeffect is, and the meaning behind the correlation coefficient in relation to your data. (paper detail below)

Step 6 – Write a paper in MLA format, explain what the data is that you analyzed (including where you got the data from), and why you thought the data might be correlated. Summarize what the graph shows about the correlation (or lack of correlation) using the terms you learned in class (positive/negative, weak/strong). Discuss the line of best fit and regression line (include the meaning of the gradient and y-intercept, correlation coefficient). Discuss why your equation is reasonable, especially how your slope number represents the rate of change you see. Make some conclusions about your data and the impact in the real world? For example: What sorts of useful applications might you be able to use the data for. What application can you use for this data? Can you make predictions based on your model that are accurate? Include a brief conclusion of the project.

Step 7 – Assemble the papers neatly together.

• Cover Page: Title, relevant graphic, name.

• Data

• Scatter Plot

• Paper

• Work Shown Section

Everything should be labeled, neatly presented and prepared as you were handing the project into your boss and looking for a promotion.

Scatter Plots and Best-Fit Lines

Grading Rubric

|Project element |Points |

|Title Page |

| Title of Project, relevant picture provide and name |4 |

|Data Table |

| between 20-50 ordered pairs in table, easy to read |5 |

| x, y values identified & labeled |2 |

|Graph |

| hand-drawn on graph paper, correct size |2 |

| scatterplot accurate to data table |2 |

| axis scales uniformly numbered |2 |

| axes labeled |2 |

| scatterplot uses available space well |2 |

| line of best fit drawn and labeled in one color |4 |

| Regression line drawn in and labeled another color |4 |

|Equation |

| equations is in slope-intercept form, simplest form |4 |

| equation accurate to the line as drawn |4 |

|Paragraph |

| describes exactly what the data are |2 |

| describes where data come from (your source) |2 |

| explains why you thought they might be correlated |2 |

| categorizes correlation (positive/negative |2 |

|strong/weak) as illustrated by graph | |

| Discusses the line of best fit and regression lines | |

|(defines the slopes and y-intercepts) and discusses the differences between the lines |5 |

| notes whether the observed correlation makes sense |2 |

| identifies any exceptional data points (outliers) |2 |

| Discusses applications to the real world |5 |

|Presentation |

| prominent and meaningful title page |2 |

| neatness & attractiveness |2 |

| spelling, punctuation & grammar |2 |

| Provided work |5 |

Total points:____70______

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