Casio fx-7400G PLUS User manual

Statistical Graphs and
Calculations
This chapter describes how to input statistical data into lists, and
how to calculate the mean, maximum and other statistical values. It
also tells you how to perform regression calculations.
1. Before Performing Statistical Calculations
2. Statistical Calculation Examples
3. Calculating and Graphing Single-Variable Statistical Data
4. Calculating and Graphing Paired-Variable Statistical Data
5. Manual Graphing
6. Performing Statistical Calculations
Chapter
7
Important!
•This chapter contains a number of graph screen shots. In each case, new data
values were input in order to highlight the particular characteristics of the graph
being drawn. Note that when you try to draw a similar graph, the unit uses data
values that you have input using the List function. Because of this, the graphs
that appears on the screen when you perform a graphing operation will prob-
ably differ somewhat from those shown in this manual.

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Chapter 7 Statistical Graphs and Calculations
1. Before Performing Statistical
Calculations
In the Main Menu, select the STAT icon to enter the STAT Mode and display the
statistical data lists.
Use the statistical data lists to input data and to perform statistical calculations.
1(GRPH) .... Graph menu
2(CALC) ..... Statistical calculation menu
3(SRT•A) .... Ascending sort
4(SRT•D) .... Descending sort
[
1(DEL) ........ Single data item delete
2(DEL•A) .... Delete all data
3(INS) ......... Insert data item
Press [to return to the previous menu.
•The procedures you should use for data editing are identical to those you use
with the list function. For details, see “Chapter 6 List Function”.
2. Statistical Calculation Examples
Once you input data, you can use it to produce a graph and check for tendencies.
You can also use a variety of different regression calculations to analyze the data.
Example To input the following two data groups and perform statistical
calculations
0.5, 1.2, 2.4, 4.0, 5.2
–2.1, 0.3, 1.5, 2.0, 2.4
1234[
1234[
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P. 8 4
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Use f , c , d and e to move
the highlighting around the lists.
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Statistical Graphs and Calculations Chapter 7
kk
kk
kInputting Data into Lists
Input the two groups of data into List 1 and List 2.
a.fwb.cw
c.ewewf.cw
e
-c.bwa.dw
b.fwcwc.ew
Once data is input, you can use it for graphing and statistical calculations.
•Input values can be up to 10 digits long (9-digit mantissa and 2-digit exponent
when using exponential format). Values in statistical data table cells are shown
only up to six digits.
•You can use the f, c, dand ekeys to move the highlighting to any cell in
the lists for data input.
kk
kk
kPlotting Data
Example To specify Graph 1 as non-draw (OFF) and Graph 3 as draw (ON)
and use Graph 3 to plot the data you input into statistical data
List 1 and List 2 above
While the statistical data list is on the display, press 1(GRPH) to display the graph
menu.
1(GRPH)
1(GPH1) ..... Graph 1 draw
2(GPH2) ..... Graph 2 draw
3(GPH3) ..... Graph 3 draw
[
1(SEL) ......... Graph (GPH1, GPH2, GPH3) selection
4(SET) ......... Graph settings (graph type, list assignments)
Press [to return to the previous menu.
•You can specify the graph draw/non-draw status, the graph type, and other gen-
eral settings for each of the graphs in the graph menu (GPH1, GPH2, GPH3).
•You can press any function key (1,2,3) to draw a graph regardless of the
current location of the highlighting in the statistical data list.
•The initial default graph type setting for all the graphs (Graph 1 through Graph 3)
is scatter diagram, but you can change to one of a number of other graph types.
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Chapter 7 Statistical Graphs and Calculations
kk
kk
kPlotting a Scatter Diagram
It is often difficult to spot the relationship between two sets of data (such as height
and shoe size) by simply looking at the numbers. Such relationships often become
clear however, when we plot the data on a graph, using one set as x-values and the
other set as y-values.
uu
uu
uTo plot a scatter diagram
Example To plot the data we input in statistical data List 1 and List 2
1(GPH1)
•The default setting automatically uses List 1 data as x-axis values and List 2 data
as y-axis values. Each set of x/ydata is a point on the scatter diagram.
•To return to the statistical data list, press Q.
kk
kk
kChanging Graph Parameters
Use the following procedures to specify the graph draw/non-draw status, the graph
type, and other general settings for each of the graphs in the graph menu (GPH1,
GPH2, GPH3).
1. Graph draw/non-draw status (SELECT)
The following procedure can be used to specify the draw (On)/non-draw (Off) status
of each of the graphs in the graph menu.
uu
uu
uTo specify the draw/non-draw status of a graph
1. While the graph menu is on the display, press [1(SEL) to display the graph
On/Off screen.
1(GRPH)
[1(SEL)
1(On) .......... Graph On (graph draw)
2(Off) .......... Graph Off (graph non-draw)
4(DRAW) .... Draw all On graphs
•Note that the S-Grph1 setting is for Graph 1 (GPH1 of the graph menu), S-Grph2
is for Graph 2, and S-Grph3 is for Graph 3.
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Statistical Graphs and Calculations Chapter 7
2. Use fand cto move the highlighting to the graph whose draw (On)/non-draw
(Off) status you want to change and press 1(On) or 2(Off).
3. To return to the graph menu, press Q.
uu
uu
uTo draw a graph
Example To draw a scatter diagram of Graph 3 only
1(GRPH)[1(SEL)
2(Off)
cc1(On)
4(DRAW)
2. General graph settings (SET)
This section describes how to use the general graph settings screen to make the
following settings for each graph (GPH1, GPH2, GPH3).
• Graph Type
The initial default graph type setting for all the graphs is scatter graph. You can select
one of a variety of other statistical graph types for each graph.
• List or Data
The initial default statistical data is List 1 for single-variable data, and List 1 and List
2 for paired-variable data. You can specify which statistical data list you want to use
to draw the graph.
• Frequency
Normally, each data item or data pair in the statistical data list is represented on a
graph as a point. When you are working with a large number of data items however,
this can cause problems because of the number of plot points on the graph. When
this happens, you can specify a frequency list that contains values indicating the
number of instances (the frequency) of the data items in the corresponding cells of
the lists you are using for x-data and y-data. Once you do this, only one point is
plotted for the multiple data items, which makes the graph easier to read.
• Mark Type
This setting lets you specify the shape of the plot points on the graph.
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Chapter 7 Statistical Graphs and Calculations
1234
1234[
uu
uu
uTo display the general graph settings (SET) screen
While the graph menu is on the display, press [4(SET) to display the general
graph settings screen.
1(GRPH)
[4(SET)
•The settings shown here are examples only. The settings on your general graph
settings screen may differ.
uu
uu
uTo select the StatGraph area
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the StatGraph item.
2. Use the function key menu to select the StatGraph area you want to select.
1(GPH1) ..... Graph 1
2(GPH2) ..... Graph 2
3(GPH3) ..... Graph 3
uu
uu
uTo select the graph type (G-Type)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the G-Type item.
2. Use the function key menu to select the graph type you want to select.
1(Scat) ........ Scatter diagram
2(xy)........... xy line graph
3(Pie) .......... Pie chart
4(Stck) ........ Stacked bar chart

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Statistical Graphs and Calculations Chapter 7
1234[
1234[
1234[
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[
1(Hist) ......... Histogram
2(Box) ......... Med-box graph
3(N•Dis) ...... Normal distribution curve
[
1(X) ............ Linear regression graph
2(Med) ........ Med-Med graph
3(X^2) ......... Quadratic regression graph
[
1(Log) ......... Logarithmic regression graph
2(Exp) ......... Exponential regression graph
3(Pwr) ......... Power regression graph
[
1(Bar) ......... Bar graph
2(Line) ........ Line graph
3(Both) ....... Bar graph and line graph
Press [to return to the previous menu.
uu
uu
uTo select the x-axis data list (XList)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the XList item.

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Chapter 7 Statistical Graphs and Calculations
2. Use the function key menu to select the name of the statistical data list whose
values you want on the x-axis of the graph.
1(List1) ....... List 1
2(List2) ....... List 2
3(List3) ....... List 3
4(List4) ....... List 4
[
1(List5) ....... List 5
2(List6) ....... List 6
Press [to return to the previous menu.
uu
uu
uTo select the y-axis data list (YList)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the YList item.
2. Use the function key menu to select the name of the statistical data list whose
values you want on the y-axis of the graph.
1(List1) ....... List 1
2(List2) ....... List 2
3(List3) ....... List 3
4(List4) ....... List 4
[
1(List5) ....... List 5
2(List6) ....... List 6
Press [to return to the previous menu.
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Statistical Graphs and Calculations Chapter 7
uu
uu
uTo select the frequency data list (Freq)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the Freq item.
2. Use the function key menu to select the frequency setting you want.
1(1) ............. Plot all data (1-to-1)
2(List1) ....... List 1 data is frequency data.
3(List2) ....... List 2 data is frequency data.
4(List3) ....... List 3 data is frequency data.
[
1(List4) ....... List 4 data is frequency data.
2(List5) ....... List 5 data is frequency data.
3(List6) ....... List 6 data is frequency data.
Press [to return to the previous menu.
uu
uu
uTo select the plot mark type (M-Type)
1. While the general graph settings screen is on the display, use fand cto
move the highlighting to the M-Type item.
2. Use the function key menu to select the plot mark you want to select.
1( )............ Plot using
2(X) ............ Plot using X
3(•) .............. Plot using •
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Chapter 7 Statistical Graphs and Calculations
1234[
1234[
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uu
uu
uTo select the data list for a pie chart, stacked bar chart, bar graph
or line graph (Data)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the Data item.
2. Use the function key menu to select the name of the statistical data list whose
values you want to use.
1(List1) ....... List 1
2(List2) ....... List 2
3(List3) ....... List 3
4(List4) ....... List 4
[
1(List5) ....... List 5
2(List6) ....... List 6
Press [to return to the previous menu.
uu
uu
uTo select the data list for a combined bar graph and line graph (Both)
1. While the graph settings screen is on the display, use fand cto move the
highlighting to the Bar item.
2. Use the function key menu to select the name of the statistical data list whose
values you want to use.
1(List1) ....... List 1
2(List2) ....... List 2
3(List3) ....... List 3
4(List4) ....... List 4
[
1(List5) ....... List 5
2(List6) ....... List 6
Press [to return to the previous menu.

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Statistical Graphs and Calculations Chapter 7
3. Use fand cto move the highlighting to the Line item.
4. Use the function key menu to select the name of the statistical data list whose
values you want to use.
1(List1) ....... List 1
2(List2) ....... List 2
3(List3) ....... List 3
4(List4) ....... List 4
[
1(List5) ....... List 5
2(List6) ....... List 6
Press [to return to the previous menu.
kk
kk
kDrawing an xy Line Graph
Paired data items can be used to plot a scatter diagram.A scatter diagram where the
points are linked is an xy line graph.
Press Qto return to the statistical data list.
kk
kk
kSelecting the Regression Type
After you graph statistical data, you can use the function menu at the bottom of the
display to select from a variety of different types of regression.
1(X) ............ Linear regression
2(Med) ........ Med-Med line
3(X^2) ......... Quadratic regression
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(G-Type)
(xy)
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Chapter 7 Statistical Graphs and Calculations
[
1(Log) ......... Logarithmic regression
2(Exp) ......... Exponential regression
3(Pwr) ......... Power regression
4(2VAR) ...... Paired-variable statistical results
Press [to return to the previous menu.
kk
kk
kDisplaying Statistical Calculation Results
Whenever you perform a regression calculation, the regression formula parameter
(such as aand bin the linear regression y= ax + b) calculation results appear on the
display. You can use these to obtain statistical calculation results.
Regression parameters are calculated as soon as you press a function key to select
a regression type while a graph is on the display.
Example To display logarithmic regression parameter calculation results
while a scatter diagram is on the display
[1(Log)
kk
kk
kGraphing statistical calculation results
You can use the parameter calculation result menu to graph the displayed regres-
sion formula.
3(COPY) ..... Stores the displayed regression formula as a graph function
4(DRAW) .... Graphs the displayed regression formula
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Statistical Graphs and Calculations Chapter 7
Example To graph a logarithmic regression
While logarithmic regression parameter calculation results are on the display, press
4(DRAW).
4(DRAW)
For details on the meanings of function menu items at the bottom of the display, see
“Selecting the Regression Type”.
3. Calculating and Graphing Single-
Variable Statistical Data
Single-variable data is data with only a single variable. If you are calculating the
average height of the members of a class for example, there is only one variable
(height).
Single-variable statistics include distribution and sum. The following three types of
graphs are available for single-variable statistics.
kk
kk
kHistogram
From the statistical data list, press 1(GRPH) to display the graph menu, press
[4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to histogram.
Input data into a list, make the required settings, and then draw the graph.
kk
kk
kBox Graph
This type of graph lets you see how a large number of data items are grouped within
specific ranges. A box encloses all the data in an area from the first quartile (Q1) to
the third quartile (Q3), with a line drawn at the median (Med). Lines (called whiskers)
extend from either end of the box up to the minimum and maximum of the data.
From the statistical data list, press 1(GRPH) to display the graph menu, press
[4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to box graph.
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P. 101
(G-Type)
(Hist)
P. 101
(G-Type)
(Box)

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Chapter 7 Statistical Graphs and Calculations
P. 101
(G-Type)
(N•Dis)
Med Q3
1234
Q1
maxX
kk
kk
kNormal Distribution Curve
The normal distribution curve is graphed using the following normal distribution func-
tion.
y= 1
(2 π)xσ n
e
–2xσn
2
(x–x)
2
The distribution of characteristics of items manufactured according to some fixed
standard (such as component length) fall within normal distribution. The more data
items there are, the closer the distribution is to normal distribution.
From the statistical data list, press 1(GRPH) to display the graph menu, press
[4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to normal distribution.
kk
kk
kDisplaying Single-Variable Statistical Results
Single-variable statistics can be expressed as both graphs and parameter values.
When these graphs are displayed, the menu at the bottom of the screen appears as
below.
1(1VAR) ...... Single-variable calculation result menu
Pressing 1(1VAR) displays the following screen.
1(1VAR)
minX

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Statistical Graphs and Calculations Chapter 7
The following describes the meaning of each of the parameters.
_
x...................... Mean of data
Σx.................... Sum of data
Σx2.................. Sum of squares
xσn.................. Population standard deviation
xσn-1 ................ Sample standard deviation
n...................... Number of data items
minX................ Minimum
Q1 ................... First quartile
Med ................. Median
Q3 ................... Third quartile
maxX............... Maximum
Mod ................. Mode
•Press 4(DRAW) to return to the original single-variable statistical graph.
kk
kk
kPie Chart
From the statistical data list, press 1(GRPH) to display the graph menu, press [
4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to pie chart. Next, move the highlighting to “Display” and then press
1or 2to select the pie chart data format.
1(%) ............ Displayed values show what percentage of the total data each
pie segment represents.
2(Data) ....... Displayed values show actual data.
Press Qto draw the chart.
Example To input the following data into List 1 and use it to draw a pie
chart: 18.0, 13.5, 4.5, 31.5, 22.5
1(GRPH)[4(SET)
1(GPH1)c
3(Pie)c
1(List1)c
1(%)Q
1(GRPH)1(GPH1)
•Apie chart can have up to eight data items. Attempting to draw a pie chart for a
list that has more than eight data items causes an error (Dim ERROR).
•Only positive data can be included in a pie chart. Attempting to draw a pie chart
for a list that includes negative data causes an error (Ma ERROR).
•View Window settings are not applied to pie charts.
•Apie chart cannot be superimposed with another graph.
•Values appearing on a pie chart are automatically assigned to the corresponding
variables (A, B, C, etc.)
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Chapter 7 Statistical Graphs and Calculations
•Performing a trace operation (!1 (TRCE)) while a pie chart is on the display
causes the pointer to appear at the topmost segment. Pressing eand dmoves
the pointer to neighboring segments.
•While a pie graph is on the display, you can toggle between the two data formats
(percent and data) by pressing !4 (CHNG).
•You cannot draw multiple pie charts on the same screen.
•Percent values shown on pie charts are cut off to two decimal places.
uu
uu
uPerforming Mathematical Operations Using Pie Chart Data
Pressing !3 (GSLV) causes the cursor to appear at the bottom of the screen.
You can then perform mathematical operations using the chart’s data.
Example To perform the operation A + B
After drawing the pie chart, perform the following operation.
!3(GSLV)
aA+aB
w
The result shows that A and B account for 35% of the data.
kk
kk
kStacked Bar Chart
From the statistical data list, press 1(GRPH) to display the graph menu, press [
4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to stacked bar chart.
Press Qto draw the chart.
Example To input the following data into List 1 and use it to draw a stacked
bar chart: 18.0, 13.5, 4.5, 31.5, 22.5
1(GRPH)[4(SET)
1(GPH1)c
4(Stck)c
1(List1)Q
1(GRPH)1(GPH1)
•Astacked bar chart can have up to eight data items. Attempting to draw a stacked
bar chart for a list that has more than eight data items causes an error (Dim
ERROR).
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(Stck)

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Statistical Graphs and Calculations Chapter 7
•Only positive data can be included in a stacked bar chart. Attempting to draw a
stacked bar chart for a list that includes negative data causes an error (Ma ER-
ROR).
•Astacked bar chart cannot be superimposed with another graph.
•View Window settings are not applied to stacked bar charts.
•The following display shows what happens if you perform a trace operation (!
1(TRCE)) while a stacked bar chart is on the display.
•Pressing fand cmoves the highlighting up and down within the same graph.
•If you have multiple stacked bar charts on the screen, use dand eto move
between them.
uu
uu
uLinking the Segments of Stacked Bar Charts with Connecting Lines
While multiple stacked bar charts are on the display, press !4(CNCT) to link
their segments with connecting lines.
Redraw the stacked bar charts to clear the connecting lines.
kk
kk
kBar Graph
From the statistical data list, press 1(GRPH) to display the graph menu, press [
4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to bar graph.
Press Qto draw the graph.
P. 101
(G-Type)
(Bar)
!1(TRCE)
R

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Chapter 7 Statistical Graphs and Calculations
Example To input the following data into List 1 and use it to draw a bar
graph: 18.0, 13.5, 4.5, 31.5, 22.5
1(GRPH)[4(SET)
1(GPH1)c
[[[[1(Bar)c
1(List1)Q
1(GRPH)1(GPH1)
•Abar graph can have up to 14 data items. Attempting to draw a bar graph for a
list that has more than 14 data items causes an error (Dim ERROR).
•The x-axis of a bar graph is fixed. The y-axis is controlled by View Window set-
tings only when Man (manual) is specified for the S-Wind (Statistical Graph View
Window Setting) on the Set Up screen.
•Abar graph can be superimposed with a line graph only. This is done by selecting
3(Both) while specifying the graph type.
•Pressing !1(TRCE) while a bar graph is on the display activates the trace
operation. Use dand eto move the pointer.
•You cannot draw multiple bar graphs on the same screen.
kk
kk
kLine Graph
From the statistical data list, press 1(GRPH) to display the graph menu, press [
4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to line graph.
Press Qto draw the graph.
Example To input the following data into List 1 and use it to draw a line
graph: 18.0, 13.5, 4.5, 31.5, 22.5
1(GRPH)[4(SET)
1(GPH1)c
[[[[2(Line)c
1(List1)Q
1(GRPH)1(GPH1)
•Aline graph can have up to 14 data items. Attempting to draw a line graph for a
list that has more than 14 data items causes an error (Dim ERROR).
•The x-axis of a line graph is fixed. The y-axis is controlled by View Window set-
tings only when Man (manual) is specified for the S-Wind (Statistical Graph View
Window Setting) on the Set Up screen.
•Aline graph can be superimposed with a bar graph only. This is done by selecting
3(Both) while specifying the graph type.
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Statistical Graphs and Calculations Chapter 7
•Pressing !1(TRCE) while a line graph is on the display activates the trace
operation. Use dand eto move the pointer.
•You cannot draw multiple line graphs on the same screen.
kk
kk
kBar Graph and Line Graph
From the statistical data list, press 1(GRPH) to display the graph menu, press
[4(SET), and then change the graph type of the graph you want to use (GPH1,
GPH2, GPH3) to Both.
When Auto is specified for the S-Wind (Statistical Graph View Window Setting) item
on the Set Up screen, you can next move the highlighting to the AutoWin item and
press 1, 2, or 3to make one of the following settings.
1(Sep.G) ..... This setting causes each graph to be drawn in different areas
of the display, without superimposing them. The two graphs
share the same x-coordinates, however, and the x-axis is dis-
played for the bar graph only.
2(O.Lap) ..... This setting superimposes the two graphs on each other. Each
graph, however, can have its own independent y-axis values.
3(Norm) ...... This setting also superimposes the two graphs, with both us-
ing the same x- and y-coordinates.
Press Qto draw the graph.
Example Draw a graph that shows precipitation in
a certain city as a bar graph and average
temperature as a line graph.
Input the precipitation data into List 1 and
the temperature data into List 2. Use the
following procedure to draw the graph.
1(GRPH)[4(SET)
1(GPH1)c
[[[[3(Both)c
1(List1)c
2(List2)c
1(Sep.G)Q
1(GRPH)1(GPH1)
•Pressing !1(TRCE) while the graph is on the display activates the trace
operation. Use dand eto move the pointer.
•You cannot draw multiple bar and line graphs on the same screen.
List 1 List 2
1100 5
2150 4
3200 11
4400 16
5300 20
6800 24
7750 31
8200 32
9350 29
10 500 24
11 80 18
12 80 6
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(G-Type)
(Both)
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Chapter 7 Statistical Graphs and Calculations
4. Calculating and Graphing Paired-
Variable Statistical Data
Under “Plotting a Scatter Diagram,” we displayed a scatter diagram and then per-
formed a logarithmic regression calculation. Let’s use the same procedure to look at
the six regression functions.
kk
kk
kLinear Regression Graph
Linear regression plots a straight line that passes close to as many data points as
possible, and returns values for the slope and y-intercept (y-coordinate when x= 0)
of the line.
The graphic representation of this relationship is a linear regression graph.
Q1(GRPH)[4(SET)c
1(Scat)
Q1(GRPH)1(GPH1)
1(X)
4(DRAW)
The following are the meanings of the above parameters.
a...... Regression coefficient (slope)
b...... Regression constant term (y-intercept)
r...... Correlation coefficient
(G-Type)
(Scat)
(GPH1)
(X)
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