Classic Financial II manual · Chapter 11 of 16

Statistics and regression

Enter x and y data, then find means, standard deviations, regression lines and forecasts.

11.1Enter data points#

Press 2NDDATA7 (DATA). Lines alternate X01, Y01, X02, Y02 and so on. Type a value and press ENTER, then ↓ to the next line. Y values default to 1, so for one-variable statistics you only need X. 2NDDEL↑ deletes a point, 2NDINS↓ inserts one, and 2NDCLR WORKCE/C clears all data. Up to 50 points can be entered.

The DATA worksheet. The display shows: X01= 0.00. — The DATA worksheet.

Example 11.1

Enter two points

Enter x = 5, then move down to its y line.
2NDDATA75ENTER↓

Example 11.2

Clear the data

Enter points, then clear the sheet with 2ND CE/C.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDCLR WORKCE/C

11.2Read the statistics#

Press 2NDSTAT8 (STAT). The first line chooses the method: LIN (a straight line), Ln, EXP, PWR or 1-V (one variable). Change it with 2NDSETENTER. Then press ↓ for n, x̄, Sx, σx, ȳ, Sy, σy, a, b and r, then X' and Y' (forecasts) and the sums Σx, Σx², Σy, Σy² and Σxy.

\bar x=\frac{\sum x}{n},\quad S_x=\sqrt{\frac{\sum (x-\bar x)^2}{n-1}},\quad \sigma_x=\sqrt{\frac{\sum (x-\bar x)^2}{n}}

Mean, sample and population standard deviation.

y=a+bx,\qquad b=\frac{n\sum xy-\sum x\sum y}{n\sum x^2-(\sum x)^2},\qquad a=\bar y-b\bar x

The least-squares line (method LIN).

The STAT worksheet starts at the method line. The display shows: LIN. — The STAT worksheet starts at the method line.

Example 11.3

Number of points

Enter five points (1,2) (2,4) (3,5) (4,4) (5,5) then open STAT and go down once.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓

Example 11.4

Mean of x

Press down once more.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓

Example 11.5

Sample standard deviation

Sx is on the next line.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓

Example 11.6

Slope and intercept

For LIN, a is the intercept and b is the slope.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓↓↓↓↓↓

Example 11.7

The line's slope b

One line further.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓↓↓↓↓↓↓

Example 11.8

Correlation

Show nine decimals, then go to r.
2NDFORMAT.9ENTER2NDQUITCPT2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓↓↓↓↓↓↓↓

Example 11.9

Sum of x

Σx is a few lines below.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓↓↓↓↓↓↓↓↓↓↓

11.3Forecast with the line#

X' and Y' give forecasts from the fitted curve. To forecast y from a known x, type the x on the Y' line, press ENTER, then press CPT. To forecast x from a known y, do the same on the X' line.

Example 11.10

Forecast y for x = 6

Go to Y', type 6, enter, then CPT.
2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT8↓↓↓↓↓↓↓↓↓↓↓6ENTER↓CPT

Example 11.11

Other curves

Choose Ln with 2ND ENTER, then look at a.
2NDFORMAT.9ENTER2NDQUITCPT2NDDATA71ENTER↓2ENTER↓2ENTER↓4ENTER↓3ENTER↓5ENTER↓4ENTER↓4ENTER↓5ENTER↓5ENTER↓2NDSTAT82NDSETENTER↓↓↓↓↓↓↓↓

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