TI-83 Plus--regression



TI-83 Plus

Regression with Inference

IPS 4/e Example 2.4, p. 110

Let’s investigate whether the apparent linear relationship between humerus and femur is statistically significant.

First row: x = Archaeopteryx femur length (cm)

Second row: y = Archaeopteryx humerus length (cm)

|Femur | 38 | 56 | 59 | 64 | 74 |

|Humerus | 41 | 63 | 70 | 72 | 84 |

TI-83 Plus Least-Squares Regression

Enter the x values into list L1. (Use STAT 1:Edit.)

Enter the y values into list L2.

Then do this:

STAT CALC 8 2nd L1 ,2nd L2 ENTER

to get 8:LinReg(a+bx).

Scatterplot with Regression Line

Instead of the above, do the following:

STAT CALC 8 2nd L1 ,2nd L2 , VARS Y-VARS 1 1 ENTER

This will make the regression equation Y1 = a + bX.

Plotting the scatterplot and regression line

Use 2nd STAT PLOT to turn on only Plot1, say, select the scatterplot, and make the Xlist L1 and the Ylist L2. You may get your TI-83 Plus to calculate Xmin, Xmax, Ymin, and Ymax by using 2-VarStats:

STAT CALC 2 L1 , L2

In WINDOW make sure that the Xmin, Xmax, Ymin, and Ymax values include all your scatterplot data.

GRAPH will show your scatterplot with the regression line drawn in.

Residual plot

After the TI-83 Plus has calculated the regression line, the residuals are stored in the LIST screen.

To get a residual plot, then, do the following.

2nd LIST 7 STO( 2nd L3 ENTER

(This stores the residuals, 7:RESID, in L3 or other free list. Do not destroy your Xlist.)

2nd STAT PLOT

Select Plot1 (or your previous plot) and change Ylist to L3.

Y=

Deselect your regression line Y1 by “unhighlighting” the = symbol.

STAT CALC 1 Use 1-Var Stats on L3 to find the min and max.)

WINDOW

Set Ymin and Ymax to include your residuals.

GRAPH

Testing whether the correlation coefficient (or regression line slope) is zero

Simple linear regression model:

The mean y value for each x is given by (y = ( + ( x and the standard deviation of y for every x is the same, namely (. The population correlation coefficient is (.

You can test H0: ( = 0 (or H0: ( = 0) against one- and two-sided alternatives without repeating all of the above steps.

Enter your x and y values into two lists as above.

To simulate a fresh start in our example, let’s make new copies of our original lists.

L1 STO( L4 ENTER

L2 STO( L5 ENTER

STAT TEST E Scroll up or down to E and ENTER, or press ALPHA E to get E:LinRegTest.

Xlist: L4

Ylist: L5

Freq: 1

( or (: (0 0 Select inequality.

RegEQ: Y1 Do this: VARS Y-VARS 1 1 ENTER

Calculate ENTER

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