technology activity 3_MAT-121
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School
Thomas Edison State College *
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Course
121
Subject
Mathematics
Date
Feb 20, 2024
Type
docx
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Uploaded by MegaKnowledge13137
MAT-121: COLLEGE ALGEBRA
Technology Activity 3
You are now going to investigate linear regression using Geogebra classic
. For help with this activity, check out the instructional video
and accompanying example
.
Select a data set from this folder
. Post a message to the discussion forum indicating which data set you have chosen so that your classmates will know to select other sets. (
Note:
Data sets are selected on a first-come basis. If a classmate has already chosen a data set you had wanted to use, please select a different one.)
Data Set Name:
Testicular Cancer Data Set
Step 1: Select the Spreadsheet
option. You only need to display the first two columns. To do this, move the cursor to the vertical line separating the spreadsheet and coordinate plane and drag it to the left until only columns A and B are shown on the spreadsheet.
Step 2: Copy columns, t
and New Cases,
of your cancer data. Click in cell A1 of the spreadsheet in Geogebra and paste the data. Step 3: Now, you need to take the data and create ordered pairs. Select all the data, click on the List
icon
and select the List of Points
option.
You’ll get a popup box which states the default name of the list of points and all the ordered pairs.
Click the OK
button. The points are now displayed in the graph area (you may have to zoom out to see them).
Note:
If there are no grid lines on your graph, click on the Tools
icon, click the Grid
icon and then click the
Show the grid
icon.
The grid will be displayed. This will allow you to determine the maximum and minimum values for our y axis (the x
axis will be based on the number of data points we have.)
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Step 4: Set the axes values based on your data set. Click on the Tools
icon in the upper right area of the grid and click on the settings icon.
You can now set the x
and y
axes values based on your data set values. Since you are mapping 1975 to t
= 0 and the last year, 2018, to t
= 43, you can have x
values go from -1 as the “x Min” value and 45 for the
“x Max” value. This is the same for any data set chosen. Your y
values will be determined by your data values in the columns New Cases
and Death Rates
. For “y Min” set it to a value of -0.1, and for “y Max” set it to 5 more than the largest value in either one of these columns.
You should have a scatter plot that looks something like the following. (Note: If your data set values decrease you will have a scatter plot with a negative slope.)
Step 5: You will now visually select your best line of fit. Click on the Line
tool icon and select Line
. If your data set values increase, click on the point in the lower left of the data points that will represent
(
x
1
, y
1
)
. Finish the line by clicking again in the upper right of the data points to complete your visual line of best fit (this will represent the second point for our equation (
x
1
, y
1
)
.) If your data set values decrease
, click on the point in the upper left of the data points that will represent
(
x
1
, y
1
)
. Finish the line by clicking again in the lower right of the data points to complete your visual line of
best fit (this will represent the second point for our equation (
x
1
, y
1
)
.) Remember, your visual line of best fit should be drawn through the maximum number of points on a scatter plot balancing about an equal number of points above and below the line.
Move your mouse cursor over the line until the “finger” mouse pointer is displayed. Right click on the line and then click on “Show label” to have the label for the line, probably f
, in the lower left of the line.
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In order to see the equation of the line that Geogebra calculated, click on the Tools
icon, click on the 3 vertical dots, then click on the Algebra
option. Geogebra will display the equation of your line in the Input
area on the left. You may need to adjust the Algebra
area and the Spreadsheet
area to be able to see the complete equation as well as your data points.
If your equation is not displayed after your data points then scroll up to the top (sometimes Geogebra will place it at the top of all the data.)
Step 6: Enter the equation from your visual best line of fit below.
Standard form: -2.92x + 38y = 127.8
Enter the algebra steps to rewrite your equation above in y
-intercept form.
−2.92
x + 38
y = 127.8
Add 2.92
x
to both sides.
38
y = 127.8 + 2.92
x
The equation is in standard form.
38
y
=73
x
+127.8
25
Divide both sides by 38.
38
y
= 73
x
+127.8
25 _
38 38
Dividing by 38 undoes the multiplication of 38.
y = 73
x
+ 127.8
25 _
38
Divide 127.8+2573
x
by 38.
y
=73
x
+ 639
950 190
Y
-intercept form: y = 3
x
+ 639
38 190
Y = 0.07x + 3.36
Step 7: You are now ready to have Geogebra determine your best line of fit. Click on the Perpendicular Line
tool icon and select Best Fit Line
.
Select the region you want Geogebra to determine the best fit line. Click in the upper left corner or your scatter plot and drag your mouse down to include the lower right area.
After you have selected your region, lift your finger off the left mouse button and the line will appear in your grid along with its equation to the left.
Your lines won’t exactly match up, but there will probably be an area in the middle where the lines cross as shown above.
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Step 8: Enter the best fit line Geogebra determined.
Y
-intercept form: y = 0.06x + 4
Step 9: Compare your visual best line of fit to Geogebra’s best line of fit. Give a brief discussion on how close the estimates were. The best fit line and the visual lines were close in the sense that they both went through a majority of the points but the starting point of the best fit line started higher and ended lower than my visual line. According to my Y-intercept form, my x value in decimal form was about 0.07 while the best fit line had an
x value of 0.06. My (b) value was about 3.36 while the best fit line (b) value was 4.
Save your graph by clicking on the menu button in the top right and select Export Image
, then Download.
Now, you will find the best line of fit using the Death Rates
column data. To delete the two lines and data points, select column B in your spreadsheet, right-click and select Delete Column B.
Step 10: Copy the Death Rate
column of your cancer data and paste into column B of the spreadsheet in Geogebra. Repeat Steps 3 through 7 and fill in the information below for the Death Rate data.
Step 11: Enter the equation from your visual best line of fit below:
Standard form: 0.49x + 28y = 20.72
Enter the algebra steps to rewrite your equation above in y
-intercept form.
0.49x + 28y = 20.72
Subtract 0.49x from both sides
0.49x + 28y = 20.72
-0.49x -0.49x
28y = 20.72 – 0.49x
28y = 20.72 – 49x
100
28y = 20.72 – 49x
_ 100
28
28
y = - 7x
+ 37
400 50
Y
-intercept form:
y = - 7x
+ 37
400 50
y = -0.0175x + 0.74
Step 12: Enter the best fit line Geogebra determined below:
Y
-intercept form: y = -0.01x + 0.49
Step 13: Compare your visual best line of fit to Geogebra’s best line of fit. Give a brief discussion on how close the estimates were. The estimated line and GeoGebra lines were close. The slope is similar due to them being -0.01 for the best fit line and -0.0175 (-0.02) for the visual best fit line. Both lines decrease and show a similar relation to each other, but they are not parallel. They still intersect around point A1 (24,0.28) but the best visual line starts higher and decreases sooner. Save your graph by clicking on the menu button in the top right and select Export Image
, then Download.