PROJECTOR 1
Business Graphics,
Forecasting and
Presentation System
48K ZX Spectrum
PROJECTOR 1 was developed by Computer Aided Training Services Ltd
for McGraw-Hill. Key points font by Image Systems.
© 1984 McGRAW-HILL Book Company Limited
This tape is copyright. You may not record or copy any part or parts
of this tape by any means whatsoever. Hiring or lending this software
is prohibited without the written permission of the Publisher.
This software is compatible with Interface 1 and makes use of
Microdrives, if available, for files. However, this does not imply that
permission is granted to transfer, copy, or otherwise re-record the
program, other than files generated as described in this booklet.
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PROJECTOR 1
Introduction
PROJECTOR 1 is an advanced business graphics, forecasting and presentation
system. It provides a wide range of facilities, and although it is designed to be as
simple to use as possible, it is worth spending a little time getting to know it.
Load the tape by typing
LOAD "projector"
then start the tape and press ENTER.
After the tape has been running for a short time, you will obtain the title page,
plus a message "STOP THE TAPE". Stop the tape at this point, and press ENTER
to see the printer menu. This asks you for information about the kind of printer
interface and printer you are using. Select the system you require by pressing the
relevant number key. The printer is needed only if you want to copy the graphic
images generated by PROJECTOR 1 onto paper.
Restart the tape when asked.
The program will search for the relevant print routine on the tape before
loading the main part of PROJECTOR 1.
PROJECTOR 1 is a long and complex program, and takes about 5 minutes to
load from the tape. The title screen will appear, followed by a "data now loading"
message as the demonstration program is loaded into the computer. After the
"stop the tape" message, the title page will be replaced by the main menu - 14
options are available.
Select the menu option you require by using the up or down cursor keys (CAPS
SHIFT with 6 or 7) to move the red cursor until it is opposite the option you want.
It is possible to get straight to two of the most commonly needed options more
quickly. You can move the cursor directly to "New Data" a nd "Directory" by using
CAPS SHIFT with 8 (right arrow) and CAPS SHIFT with 5 (left arrow)
respectively.
It is best to begin with the demonstration, which shows you some of the
capabilities of PROJECTOR 1. Select "Play Presentation" and press ENTER.
Type in the name "demo1" (without the quote marks) and press ENTER. In
answer to the question "Breakable?" type 'y' and ENTER. PROJECTOR 1 will
now play through its demonstration. Sit back and enjoy it. If you want to stop the
presentation at any time, press CAPS SHIFT with SPACE (BREAK), which will
take you straight back to the main menu.
Follow the next part of these instructions carefully, as they take you
step-by-step through the process of loading and displaying your own data.
Delete data
Select the "Dire ctory" option as above. You will be given three options: begin by
selecting the "Delete all data" option by moving the cursor over it and pressing
ENTER. In answer to the "Sure?" prompt, answer 'y' and press ENTER again.
This deletes all data (at this stage, the demonstration) from the memory. Now,
with a clean sheet, you can enter some data of your own.
New data
Select this option from the main menu. In using PROJECTOR 1, data is typed in
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using one of a range of formats:
by DAYS, WEEKS, MONTHS, QUARTERS or YEARS;
as ORDINARY numbers:
as PAIRS of values - this format is used for an xy graph, or for pairs of
histograms such as you might use when comparing two sets of values.
You do not decide at this stage how you want to display the data. The various
display options draw on the data when you use them. Start by entering some
simple values. Try entering four quarterly values: follow the screen prompts to
select the QUARTERLY option, starting with the first quarter and any year you
like. The data entry chart will appear on the screen, with quarters listed
automatically. Enter the data for the first four quarters - try values of 15, 8, 25
and 30 as a start. Simply type in each number, followed by ENTER. After
entering the numbers, use STOP (SYMBOL SHIFT with A) to finish. You are
asked to give a name for the data - use any name you like, up to nine characters,
but for this example type "test" then ENTER. There is a short pause while the data
is checked and written into memory, at the end of which you are returned to the
main menu.
You are now ready to try out some of the display functions.
Graph
When you select this option, you are asked which data you want to use; as the only
data in the computer at the moment is "test", use that! A sub-menu shows a range
of options available for the graph. First type in a title for the graph, ("Quarters"),
and for the moment skip through the vertical and horizontal axis options by
pressing ENTER for each. Then you can select the functions you want, using 'y' or
'n' for yes and no, and pressing ENTER after each selection. You can use the
cursor keys to go up and down the list. Start by setting up a simple graph, without
using the "Fit line" or "Fit curve' options. Use STOP when you have finished. The
graph will then be displayed as you have requested. Pressing ENTER again will
return you to the main menu, after flashing on the screen a reference number for
the graph. As this is the first graph, the reference will be "g1".
Now select "Graph" from the main menu again, and try some of the other
options, perhaps joining the points or adding a background grid.
Fit line and fit curve
These options are selected from within the "Graph" option. They represent one of
PROJECTOR 1's most valuable facilities, that of fitting a calculated line or curve
to a set of values. If you also select "Display statistics" option, then after you have
pressed ENTER to end the display, a page of statistics will appear, indicating the
equation and the degree of fit of the line or curve. Note that the calculation of the
curve can be quite complicated, and it may take the computer a little while to work
it out.
Try a few variations on your graph, using the same data for now.
Histograms
Next, try the "Histograms" option. Once again, you get a sub-menu of options. Full
details of the options are given in the "Summary of Functions" which follows. To
begin with, move the cursor down to "title" and type in "Quarters", which leaves
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all the other options at their default values. Use STOP, and your histogram will
appear. Pressing ENTER will store it in memory. Note that histograms are
referenced automatically in the same way as graphs, but using "h1", "h2", etc.
Pie-charts
Try this option, too. The chart is constructed automatically from your data, and
percentages of the total are added automatically. With pie -charts you also have
the option to add text to the drawing, in the form of captions or explanatory notes.
If you make a mistake, note that PROJECTOR 1 does not let you use DELETE;
you have to move back with the cursor and overtype. Pie -charts are referenced
automatically in a series of "p1", "p2", etc. Pie -chart colours can be selected, but
adjacent sectors are always shown in contrasting types of shading, so that the
pie-chart will be understandable when copied to a printer.
Presentations
If you now go to the "Directory" option, and choose "View data", you will see your
data and all the different graphs, histograms and pie -charts that you have made
from it are referenced. You can put together a presentation using any of these. Go
back to the main menu (with ENTER or STOP) and select "Build/modify
presentation". Choose the option to "build", and (assuming that you have at least
one graph, histogram, and pie -chart) put together a presentation consisting of g1,
h1, p1. The format for entering this information is the same as for data entry. Use
STOP to end data entry. You will be asked whether you want a manual or
automatic presentation - begin with a manual one. Give the demonstration any
name up to nine characters.
To replay the presentation, select "Play presentation" from the main menu, and
proceed just as you did to play "demo1".
Break
Pressing BREAK (CAPS SHIFT with SPACE) will produce a low rasping noise,
and will take you directly to the main menu. The only exception to this is when
playing an "unbreakable" presentation . . . from this there is no escape until it has
played its course, so use unbreakable presentations with care, especially if you
have unsaved data in the computer!
PROJECTOR 1 provides a vast range of facilities. You will by now have an
idea of the basics of using the program. The following alphabetic summary of the
program's functions expands on what you have done, and explains the rest of the
features. There is no substitute for using the program! Practice until you are
completely familiar with the way PROJECTOR 1 works, and you will discover
that it is a quick, easy and time -efficient way of producing business graphics,
presentations and projections for the future.
SUMMARY OF FUNCTIONS
In alphabetical order
Build/modify presentation
A presentation is a sequence of slides that you can replay. The unique slide
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references generated by PROJECTOR 1 were displayed at the time of creating
the slides and are held on the Directory (left arrow, that is CAPS SHIFT and 5 to
get quickly to Directory from the main menu).
Presentations can be:
automatic with a pre -set delay between slides
or manual where you have to press a key at the end of each slide.
The entry screen is similar to entering ordinary data. You enter the slide
references in sequence, for example:
k2
h1
k3
p4
k6
dweek1
k2
h1
g9
will build a sequence of 9 slides starting with key points 2 and ending with graph 9.
Both upper and lower case are acceptable for referencing the slides.
You can delete from and insert slides to the presentation by using < and >;
< deletes the entry on which the cursor is placed, and > makes a space.
However, deleting from a presentation does not delete from the Directory -
the slide could be used in another presentation.
PROJECTOR 1 does not check that all the references are in the Directory, so
you can include undeveloped slides (guess their references!). When you try to
replay a non-existent slide you will get the message DATA NOT IN
MEMORY.
For automatic presentations you can specify a number of runs, that is the
number of times the presentation is played. After the first play it simply
restarts from the beginning.
Slides can be used several times in a presentation.
A presentation itself can be referred to by using "xpres3" where "pres3" is the
presentation name.
A presentation can be included in other presentations. You can chain
presentations together:
"xpres1" contains:
k2
h1
k3
p4
k6
xpres2
and plays 5 slides immediately followed by 4 more. In effect this plays as one
presentation but two are stored on the Directory.
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"xpres2" contains:
g8
k2
h1
g9
You can also embed presentations wholly within other presentations:
"xpres1" contains:
i1
xpres3
xpres4
xpres2
i1
xpres1 could have a graphic logo, a beginning xpres3, a middle xpres4, and an end
xpres2, followed by the logo again.
This technique makes it easier to combine and update presentations. You can
have up to 5 levels of presentation at any one time but they cannot loop either
directly or indirectly, that is:
"xpres1" contains:
xpres3
xpres4
where xpres4 contains:
xpres2
and xpres2 contains:
xpres4
This is not allowed because xpres4 calls itself!
If you nest presentations they are replayed with the attributes o f the deepest
level presentation running at the time. For example, if the outer one is
automatic and the inner one is manual then the combined presentation will
start automatic, switch to manual (without warning), then back to automatic.
Directory
Directory displays a catalogue of data, slides and presentations; each is given a
unique reference by PROJECTOR 1.
To get to a second screen of the Directory press any key.
You are told the amount of free space in memory. If you run out you will have
to split your slides and presentations between more than one block of data on
tape or microdrive.
You can delete entries. The method is the same as for data entry and for
building a presentation. You refer to presentations as "xpres3" where "pres3" is
the presentatio n name and data by "ddata4". No warnings are given, apart from
when you wish to delete all entries when you am prompted "Sure?".
If you delete a presentation, its constituent slides are not deleted - they may be
used elsewhere.
Note that the data is only in memory and is NOT stored on tape until you do
Save from the main menu. If you exit PROJECTOR 1 without saving you will
be reminded to Save; it is a good precaution to save on tape frequently and to
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keep two copies on different tapes.
A fast way to get to the "Directory" from the main menu is to use right arrow,
that is CAPS SHIFT and 5; (similarly to get to "New data" use left arrow, CAPS
SHIFT 8).
There is room for about 7500 characters of data in memory, which should be
ample for most presentations. Experience has shown that this represents
approximately 50 slides depending upon the mix of slides and the size of data.
For histograms and pie charts, to save space you can delete the original data on
which they were based once they are saved as slides. However, in the case of
graphs the original data must still exist when replaying. It is advisable to keep a
copy of any deleted data.
Because a screen image takes up 6351 characters you will only have space for
one full graphic image. You can of course load different sets of data and
presentations using the LOAD facility.
Errors
You will not see many errors because PROJECTOR 1 automatically returns to
the main menu and makes a rasping noise in the rare event of finding an error. If
this happens check your data and try again. In even rarer circumstances an error
can return you to Sinclair Basic command mode. If this happens type "GOTO
menu" (key G and type "menu").
Graph
For line, scatter and line fitting.
Graphs are scaled automatically with four values marked on each axis - the
maximum, minimum and two intermediate values; the axis values are rounded
up to whole numbers.
Background grid gives lines at these x and y values to help you read off the
intermediate points on the graph.
Join up points gives a line graph; if not you get a scatter plot of the data values.
If there are too many points the data values are superimposed and your graph
will look untidy, but PROJECTOR 1 tries its best; "all options on" tends to
look overcrowded!
Fit line produces and draws the "best fit" line using the technique of least
square linear regression. In its simplest terms linear regression is a statistical
technique for doing what you would do with a ruler, a pencil and common
sense.
Fit curve produces and draws a "best fit" curve if you think this is more
appropriate. If you say yes to both then the lines overrides.
Display statistics only applies if you have fitted a line or curve. It tells you the
degree of fit - if you can understand the statistics, that is! For a layman's guide
refer to "A Word About Statistics' in this booklet. It is not important that you
understand the statistics.
ENTER or STOP terminates the graph and displays statistics if requested or
tells you the graph reference.
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< (SYMBOL SHIFT and R) as usual gets you back to options, so you can fit a
curve instead or you can try a different set of data on the latest options.
When you have finished, the graph is saved in memory exactly as it last
appeared and given a reference, for example "g5".
You can copy the completed graph to the printer. You can also copy statistics
to the printer at the end of the statistics display.
If you build the graph into a presentation you are not given the option of
replaying statistics.
Graphic image
Graphic image loads a predefined screen image from tape.
A screen image is an exact copy of any screen previously saved by the
Spectrum command SAVE "name" SCREEN$. Because there are many other
graphics/painting programs available (and due to lack of space) it was decided
not to build up this SCREEN$ image using PROJECTOR 1 itself. However,
once the graphic has been loaded into the data area PROJECTOR 1 can
replay it instantly.
You are asked to position the tape to load SCREEN$ and play.
When it is loaded, a copy of the screen image is stored away in memory; you
can then copy to the printer.
As it takes 6351 characters to store one screen in memory you will only have
room for one full screen image. Typically you will use this for a company logo
at the start and finish of a presentation.
Screen images are given a reference of i; for example "i1".
Histogram
Histograms are scaled automatically.
But you can override the scaling by changing the maximum and minimum
values. If you have negative values the horizontal axis will come in the middle
of the screen.
First horizontal and Frequency horizontal refer to the labelling of the
horizontal axis. Values of 1 and 1 put labels every bar.
The horizontal labels are generated according to the type of data. For example
Sun Mon Tue etc., for daily and Jun Jul Aug etc., for monthly.
Up to 63 bars are allowed - enough for two months' daily figures. If you use
over 10 bars then labelling 1 and 1 will look untidy. The default is 5 and 5
giving horizontal labels every 5 bars.
Surprisingly you will find that red bars on a black background with a black
border looks effective.
If the data type was pairs then you get a side by side histogram. For example,
you can compare budget against actual figures.
The labelling of the horizontal axis for this type of histogram is slightly
irregular. The frequency of horizontal labels should be an even number equal
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to twice the number of pairs you want the frequency to be, and the first
horizontal label should be an odd number equal to the bar number (1,3,5 etc.)
of the first solid coloured bar you want labelled.
Once again < (SYMBOL SHIFT and R) returns you to the options screen.
ENTER or STOP stops the histogram display and moves on; you can then save
to the printer if you wish.
Each completed histogram is given a unique reference, for example h6,
entered automatically in the Directory and stored in memory.
Key points
These are used to preview, explain and summarise other slides.
Headings are optional; if you use them you get up to 5 lines of key points; if not
you get 6.
You can have bullets, or numbers (1,2,3 etc.) or just a space before each point.
You can have blank lines simply by pressing ENTER to a point when building
the slide.
You can have a delay between uncovering each point on replay.
Up to 21 characters per line are allowed. After that the line just scrolls up and
is lost!
When typing in a key point you will know when you have gone over 21
characters because the input line scrolls up (but take account of the number of
Ms and Ws - see below).
Careful with colour combinations - red letters on cyan or yellow background
works well as does blue on cyan.
Upper and lower case letters, numbers and the characters ()!%';-+=:#?/*,.
only are allowed. Other characters will give strange output. No check is made.
All valid characters are 3 Sinclair characters high by 1 character wide, except
upper and lower case W and M which are 2 characters wide. So the 21
characters per line must be reduced by 1 for each W and M!
You can modify the heading or any point. Do not worry that t he final point
sometimes appears to be overwritten. It will be OK.
Typing ENTER on its own to a point will leave a blank line.
If you type < on its own to a point you are returned to the options screen. You
can then change the letter colour or bullets options and carry on. After
returning to the options screen, you can modify any line, but PROJECTOR 1
does not step through each line automatically. Answer 'y' to "Modify?" and
then put in the line number you want to change or add. Use this feature to
emphasise one point or for continuation lines for bullet points. You can flip
between the options and the key points screen as many times as you like using <.
STOP will terminate and save the slide: you can then copy to the printer.
It is possible, but not very interesting, to have presentations consisting solely of
key points.
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Key points are given a unique reference, for example "k4", stored in memory
and added to the Directory.
Load
Loads all of the data area from tape or microdrive into memory.
Included in data are finished slides and presentations.
It overwrites any existing data.
If a microdrive is plugged in PROJECTOR 1 asks whether you want to load
from microdrive, and if so the name of the saved data file.
On first loading PROJECTOR 1, the demonstration data area is automatically
loaded. You will probably want to overwrite this with your own data area.
Modify/View data
The main menu option to Modify/View the data works in a similar way to the
"New data" option. If you do not move the cursor away from the top left-hand
corner of the data screen PROJECTOR 1 knows that you are viewing rather
than modifying and will not ask you for a new data name.
Names and references
For any set of figures you enter and any presentation you create you are asked to
name the data or presentation (such as "demo1"). These names can be up to 9
characters and punctuation marks of your own choice. PROJECTOR 1 is
"case-blind", that is upper and lower case letters are all stored as lower case, so
"Data1-6%" is equivalent to "DATA1-6%" and "data1-6%". A check is made to
ensure that you do not use the same name twice.
Histograms, pie charts, graphs, key points and images are all given their own
unique references by PROJECTOR 1, automatically stored in the data area as
slides and automatically added to the Directory. You will see the references
displayed after each has been created.
New data
New data is typed in separately from histograms, pie charts and graphs. Before
you construct histograms, pie charts or graphs, you need to input data! But you
only need to input once - you can produce a histogram, pie chart or graph from the
same data.
Data can be input:
by DAYS, WEEKS, MONTHS, QUARTERS or YEARS
simply as ORDINARY numbers
as pairs of values for an xy graph or for a side by side histogram.
Up to 63 numbers can be entered as ORDINARY data, or 42 numbers for the
other types.
Data can be positive or negative numbers with or without a decimal point, but
numbers written in scientific notation or as fractions will not be recognised.
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For example:
31, +4 and -7.67 are all valid
but, 7.5E7 or 3/4 are not.
When inputting data:
ENTER takes you to the beginning of the next field. If the cursor is at the
beginning of a field when ENTER is pressed then the number in the
previous field is repeated,
< deletes a number (see below).
> creates a space to insert (see below).
You can move around the screen with the cursor controls should you wish
to revise an entry:
An individual character can be revised by positioning the cursor over it
and typing a new character, or can be blanked out by typing a space.
< deletes the whole entry in the field that the cursor is in, and moves all
subsequent entries up one field.
> similarly moves the current field and all subsequent ones down, and
creates a space for inserting a new entry.
STOP finishes entering data. At this stage noughts are inserted in any blank
field before the last one in which you have made an entry, and you are asked
to change any entries that are not understandable numbers. When you have
made any necessary corrections exit again with STOP.
You are asked for a data name - up to 9 characters and punctuation marks of
your choice.
If data under the name you have given already exists you are given the option
to overwrite the existing data or rename your new data.
Data can be included in a presentation by referring to it as "dweek1", where
"week1" is the data name.
Options
At various points, PROJECTOR 1 contains pre -set options which will give your
slides an attractive presentation. You can v ary these by overtyping the pre -set
values followed by ENTER. When entering colour options use the numbers 0-7
on the ZX Spectrum keyboard. At the end of each histogram, pie chart, graph or
key point slide you can return to the options screen by typing < (SYMBOL
SHIFT and R), change the options and retry until you are happy with the end
result.
If any of the options are incorrect the message "Invalid" is flashed and
PROJECTOR 1 substitutes a default value. If this is unsuitable use < to change
options.
Pie-charts
Pie-charts give automatic percentages.
You add other text by simply moving the cursor and typing.
Up to 10 slices is a realistic maximum but PROJECTOR 1 leaves this up to you.
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Narrow slices can look untidy.
When building a pie you can pull out one or more slices (or all if you wish!) for
emphasis using the Separate Slice? screen.
If you do not like the format < (SYMBOL SHIFT and R) will return you to the
options screen.
Each completed pie is given a unique reference, for example "p3", entered
automatically in the Directory and stored in memory.
You are not allowed to build a pie chart based on data that includes negative
numbers. If you try you will get the message "invalid".
When you are satisfied with the picture, press STOP; you can then copy to the
printer if you wish.
Play presentation
Presentations can be:
Automatic with a preset delay between slides.
Manual where you have to press a key at the end of each slide.
You are also given the option of making the presentation breakable or not. If it is,
then pressing BREAK at any point will return you immediately to the main menu.
If not then the only way to stop is to pull out the plug! Use the unbreakable mode
only for exhibitions and point-of-sale advertising.
For manual presentations, at t he end of each slide you can press:
t to replay This slide
l to replay the Last slide
c to Copy the slide to a printer
STOP to stop the presentation
any other key to continue to the next slide.
Project
Used to forecast data for several periods.
PROJECTOR 1 allows you to extend a line or curve beyond the current data
to predict future values. You are asked how many periods forward and
whether you want to fit a line or a curve (the defaults are 6 and a line) then
PROJECTOR 1 calculates the equation of the line or curve, and generates and
then displays the new data.
Notice that the projected values lie exactly on the line or curve and are
highlighted in yellow.
Project is not allowed for data set up in "pairs" format.
The number of projected values plus existing values must be less than or equal
to 63 or 42. If this is not the case PROJECTOR 1 reduces the number of
projected values and tells you.
You can save the projected data under a new name or by using an existing
name make it overwrite existing data.
You cannot save a projection for inclusion in a presentation; but you can graph
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the projected data and save that instead, and you can copy the projected graph
to the printer using "c".
Project is an extremely powerful and easy to use facility . . .
Save
Saves all the data area on tape or microdrive.
Make sure that you are recording, not playing (ear plug out)!
You are asked to rewind the tape and play to verify that the SAVE worked
correctly. If verify fails, the computer will make a rasping sound, then return to
the main menu. If nothing at all happens (no recording!), press BREAK
(CAPS SHIFT and SPACE) to return to the main menu and save again.
If a microdrive is plugged in (PROJECTOR 1 automatically detects this) you
are asked whether you want to save to microdrive or to tape. If you reply 'm'
then you are asked additionally for a microdrive filename to uniquely identify
the data.
Save frequently and take a second copy on a different tape or microdrive
cartridge and do not keep them in the same p lace!
Summary of keys
STOP SYMBOL SHIFT and A exits from the current screen.
move cursor CAPS SHIFT 6 or 7 select a main menu option.
then ENTER
right arrow CAPS SHIFT and 8 top of menu (New data).
left arrow CAPS SHIFT and 5 Directory.
< SYMBOL SHIFT and R at the end of a slide returns you
to the options screen.
GOTO menu G and m-e-n-u restarts the program if interrupted.
BREAK CAPS SHIFT and SPACE returns immediately to the main
menu (unless an unbreakable
presentation is running).
On data entry
< SYMBOL SHIFT and R deletes a data item.
> SYMBOL SHIFT and T inserts a data item.
ENTER moves the cursor to the next field.
ENTER on its own repeats a data item.
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A WORD ABOUT STATISTICS
by Ged Fitzgibbon
Introduction
It is by no means essential to understand statistics to use PROJECTOR 1.
Statistics are not designed to be part of a presentation. However, it is useful to
know how much confidence to place in the line or curve that the computer has
drawn, and it is possible to display (and print out) statistical information. The
following, while by no means a complete description, forms an introduction to the
subject.
Linear regression is a well known statistical technique for calculating a best line
or curve to a set of data points. This section will illustrate the method and give a
brief explanation of the figures you get with the "Display Statistics" option in
building a graph
Figure 1
You can draw any number of lines through the points. Why is any line A better
than any other line B? One reason is that the residuals, that is the errors from the
points to the fitted line, add up to a smaller number for A than for B. The measure
normally used is the sum of the squares of the residuals. The smaller the sum of the
squares the better the fit. Hence the method is often called "least squares
regression".
A line has the general equation Y = mX² + c where m and c are the values
(called coefficients) to be estimated. For a curve the method fits Y = qX² + mX + c.
sales1 curve1
Figure 2 Figure 3
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So the first output from the "Display Statistics" option is the equation:
Y = -13.429 X + 405.333 for sales1
and Y = 8.217 X² - 37.129 X + 151.891 for curve1
Once calculated, the equation can be used to predict Y for new values of X. This
is the heart of the "Project" option. When you project, it should come as no
surprise that the projected values lie exactly on the line or curve.
The remaining output from the "Display Statistics" option is concerned with the
degree of statistical confidence in the fit.
R squared
sales1 = .00967 curve1 = .979
R² is one of the best measures. It is the fraction of variation of Y explained by a
variation in X. So for the curve, R² is 0.979, that is 98% of the variation in Y is
explained by a variation in X, with 2% unpredictability. This, as you can
imagine, is an unusually good fit. On the other hand R² for sales1 is only 0.009,
that is 1% of the variation is accounted for by the regression equation with the
remaining 99% random!
Corrected R² is a slight variation on R², adjusted for the degrees of freedom -
only of interest if you understand what this means.
t statistics
sales1 curve1
constant = 1.532 constant = 3.886
X = -0.198 X = -2.48
X² = 6.76
The t statistics are measures of the reliability of the individual parts of the
equation; in general the larger they are the better. Specifically if the t statistic
for a coefficient is between +2 and -2 then the coefficient is suspect. On the
other hand if its t statistic is greater than 2 (or less than -2) then there is a 95%
chance that the coefficient is non-zero. To be precise, a t statistic for a
coefficient is an indicator of whether that coefficient is zero and thus not part of
the equation. For example if you tried a curve fit and the t statistic of the X²
coefficient was low then it is highly likely that a line (without the X²) would
give a better fit.
Standard errors
sales1 curve1
constant = 264.596 constant = 39.083
X = 67.942 X = 14.969
X² = 1.215
Standard errors show the degree of variation in each of the coefficients. Since
these are known to obey the famous "normal" statistical distribution then the
usual rules apply! There is a 66% probability that a coefficient is within one
standard error and a 95% probability that it is within 2 standard errors. For
example for the line:
Y = -13.429 X + 405.333
there is a 66% chance that the constant is 405.333 plus or minus 264.595
16
(its standard error), which means that it is between 141 and 670.
There is a 95% chance that the constant is 405.333 plus or minus 531.192
(twice its standard error), that is, between -126 and 937. In other words
the standard error is saying "your guess is as good as mine!".
Curve equation: Y = 8.217 X² - 37.129 X + 151.891
On the other hand if we look at the X² coefficient on the curve the confidence
levels are:
66%: 8.217 + or - 1.215, that is between 7.0 and 9.4
95%: 8.217 + or - 2.430 (2 standard errors), that is 5.8 to 10.6
The interplay of standard errors can be difficult to interpret. The next statistic
is of more practical use.
Standard error of the regression
sales1 curve1
284.222 35.588
This shows the expected variation in the line Y itself. 66% of the values and
hence of the data points will lie within one standard error of the line and 95%
within two standard errors. For example, if we look at curve1 (sales1 gives a
ridiculously wide variation) and take a particular value of X, say 8, then Y on
the calculated curve is:
Y = 8.217 X² - 37.129 X + 151.891, that is 380.747
There is a 66% level of confidence:
that Y lies between 380.747 + or - 35.588,
that is 345 and 416;
and a 95% level of confidence
that Y lies between 380.747 + or - 71.176 (2 standard errors),
that is 309 and 451.
F statistic
sales1 curve1
0.039 186.975
This is another overall measure of the success of the regression. Needless to
say, the higher the value the better. The degrees of freedom are needed when
you look up the value in your handy pocket book of tables of the cumulative F
distribution! To save you the trouble, there is a 99% probability that curve1
fits the points, but the least said about sales1 the better!