# 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.

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Graphene has a hexagonal structure
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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