# 12.4 Notes for the ti-83, 83+, 84 calculator  (Page 3/3)

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## To see the regression graph:

1. Access the equation menu. The regression equation will be put into Y1.

2. Access the vars menu and navigate to <5: Statistics>

,

3. Navigate to <EQ> .
4. <1: RegEQ> contains the regression equation which will be entered in Y1.

5. Press . The regression line will be superimposed over scatter plot.

## To see the residuals and use them to calculate the critical point for an outlier:

1. Access the list. RESID will be an item on the menu. Navigate to it.

, [LIST] , <RESID>

2. Confirm twice to view the list of residuals. Use the arrows to select them.

,

3. The critical point for an outlier is: $1.9V\frac{\mathrm{SSE}}{n-2}$ where:
• $n$ = number of pairs of data
• $\mathrm{SSE}$ = sum of the squared errors
• $\sum \mathrm{residual}^{2}$
4. Store the residuals in [L3] .

, , [L3] ,

5. Calculate the $\frac{\mathrm{\left(residual\right)}^{2}}{n-2}$ . Note that $n-2=8$

, [L3] , , ,

6. Store this value in [L4] .

, , [L4] ,

7. Calculate the critical value using the equation above.

, , , , , [V] , , [LIST] , , , , [L4] , , ,

8. Verify that the calculator displays: 7.642669563. This is the critical value.
9. Compare the absolute value of each residual value in [L3] to 7.64 . If the absolute value is greater than 7.64, then the (x, y) corresponding point is an outlier. In this case, none of the points is an outlier.

## To obtain estimates of y for various x-values:

There are various ways to determine estimates for "y". One way is to substitute values for "x" in the equation. Another way is to use the on the graph of the regression line.

## Distributions

Access DISTR (for "Distributions").

For technical assistance, visit the Texas Instruments website at (External Link) and enter your calculator model into the "search" box.

## Binomial distribution

• binompdf(n,p,x) corresponds to P(X = x)
• binomcdf(n,p,x) corresponds to P(X ≤ x)
• To see a list of all probabilities for x: 0, 1, . . . , n, leave off the " x " parameter.

## Poisson distribution

• poissonpdf(λ,x) corresponds to P(X = x)
• poissoncdf(λ,x) corresponds to P(X ≤ x)

## Continuous distributions (general)

• $()$ uses the value -1EE99 for left bound
•  uses the value 1EE99 for right bound

## Normal distribution

• normalpdf(x,μ,σ) yields a probability density function value (only useful to plot the normal curve, in which case " x " is the variable)
• normalcdf(left bound, right bound, μ,σ) corresponds to P(left bound<X<right bound)
• normalcdf(left bound, right bound) corresponds to P(left bound<Z<right bound) - standard normal
• invNorm(p,μ,σ) yields the critical value, k: P(X<k) = p
• invNorm(p) yields the critical value, k: P(Z<k) = p for the standard normal

## Student-t distribution

• tpdf(x,df) yields the probability density function value (only useful to plot the student-t curve, in which case " x " is the variable)
• tcdf(left bound, right bound, df) corresponds to P(left bound<t<right bound)

## Chi-square distribution

• Χ 2 pdf(x,df) yields the probability density function value (only useful to plot the chi 2 curve, in which case " x " is the variable)
• Χ 2 cdf(left bound, right bound, df) corresponds to P(left bound<Χ 2 <right bound)

## F distribution

• Fpdf(x,dfnum,dfdenom) yields the probability density function value (only useful to plot the F curve, in which case " x " is the variable)
• Fcdf(left bound,right bound,dfnum,dfdenom) corresponds to P(left bound<F<right bound)

## Tests and confidence intervals

Access STAT and TESTS .

For the Confidence Intervals and Hypothesis Tests, you may enter the data into the appropriate lists and press DATA to have the calculator find the sample means and standard deviations. Or, you may enter the sample means and sample standard deviations directly by pressing STAT once in the appropriate tests.

## Confidence intervals

• ZInterval is the confidence interval for mean when σ is known
• TInterval is the confidence interval for mean when σ is unknown; s estimates σ.
• 1-PropZInt is the confidence interval for proportion
The confidence levels should be given as percents (ex. enter " 95 " or " .95 " for a 95% confidence level).

## Hypothesis tests

• Z-Test is the hypothesis test for single mean when σ is known
• T-Test is the hypothesis test for single mean when σ is unknown; s estimates σ.
• 2-SampZTest is the hypothesis test for 2 independent means when both σ's are known
• 2-SampTTest is the hypothesis test for 2 independent means when both σ's are unknown
• 1-PropZTest is the hypothesis test for single proportion.
• 2-PropZTest is the hypothesis test for 2 proportions.
• Χ 2 -Test is the hypothesis test for independence.
• Χ 2 GOF-Test is the hypothesis test for goodness-of-fit (TI-84+ only).
• LinRegTTEST is the hypothesis test for Linear Regression (TI-84+ only).
Input the null hypothesis value in the row below " Inpt ." For a test of a single mean, " μ∅ " represents the null hypothesis. For a test of a single proportion, " p∅ " represents the null hypothesis. Enter the alternate hypothesis on the bottom row.

#### Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
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