BA II Plus Linear Regression: Build a Forecast with STAT Mode

In this tutorial

The two STAT-mode keys: DATA and STAT
Entering and editing X/Y data pairs
Reading slope, intercept and correlation
Example 1: forecasting sales from ad spend (perfect fit)
Example 2: a real-world fit with noise
Predicting with Y' and X'
Common mistakes and error traps

The two STAT keys: DATA and STAT

The statistics functions live on two keys:

DATA — press [2nd] then [7] to open the data-entry worksheet. The display shows X01=, ready for the first x-value.
STAT — press [2nd] then [8] to open the statistics worksheet, which lists every statistic, including a, b, r, X' and Y'.

By default the regression type is LIN (linear). You can toggle to Ln, Exp, Pwr or 1-V (single-variable) with [2nd] then [SET] while in the STAT worksheet.

Entering data pairs

Press [2nd] then [7] (DATA).
Press [2nd] then [CLR WORK] to erase old data.
At X01, enter the first x-value, press [ENTER].
Scroll down to Y01, enter the first y-value, press [ENTER].
Scroll down — X02 appears. Enter the second pair the same way, then the third, and so on.
Use ↑ to go back and fix a typo; press [2nd] then [DEL] to delete the pair shown on screen.

Example 1: forecasting sales from advertising spend

Five quarters of ad spend (in $1,000) and sales (in $1,000):

Ad spend (x)	Sales (y)
10	100
20	150
30	200
40	250
50	300

Press [2nd] then [7], then [2nd] then [CLR WORK].
Enter the five pairs as shown: 10 [ENTER] 100 [ENTER], 20 [ENTER] 150 [ENTER], and so on.
Press [2nd] then [8] (STAT).
Scroll down past n=5 and the mean/standard-deviation lines.
At a=, read 50 — the intercept.
Scroll to b=, read 5 — the slope: every extra $1,000 of ad spend adds $5,000 of sales.
Scroll to r=, read 1.00 — a perfect linear relationship.
Scroll to Y'=, enter 60 and press [CPT] — the forecast for $60,000 of ad spend is 350 ($350,000).

The fit is perfect by construction: sales = 50 + 5×spend. It confirms the mechanics — Y' plugs the x you type into the fitted line.

Example 2: a noisy real-world fit

Real data is never this clean. Take five observations:

x	y
1	2.1
2	4.9
3	7.2
4	9.8
5	12.5

Clear DATA with [2nd] then [7], then [2nd] then [CLR WORK].
Enter the five pairs.
Press [2nd] then [8] and scroll to the regression line:

a= — −0.41 (intercept)
b= — 2.57 (slope: y rises about 2.57 per unit of x)
r= — 0.9997 (very strong, but not exactly 1 because the points do not sit on a perfect line)

Forecast y at x = 6: scroll to Y'=, enter 6, press [CPT] — the display reads about 15.01 (−0.41 + 2.57 × 6).

Predicting with Y' and X'

Y' predicts the dependent variable from a new x: type the x, press [CPT].
X' works in reverse — type a target y and the calculator returns the x the model implies (useful for breakeven-style questions).

These are the keys CFA questions about forecasting use: given historical market returns and a new beta, what return does the model predict? Enter the historical pairs, then let Y' do the plugging.

Regression variants: Ln, Exp, Pwr

If the scatterplot curves, toggle the model with [2nd] then [SET] inside the STAT worksheet: Ln fits y = a + b·ln(x), Exp fits y = a·e^b·x, and Pwr fits y = a·x^b. The a, b and r lines adapt automatically. Pick the model with the r closest to ±1, not the fanciest name.

Common mistakes and error traps

Old data left in the registers. Always [2nd] then [CLR WORK] before entering a new dataset — leftover pairs change every statistic.
Entering x into Y. X comes first, then Y; swapping every pair flips nothing visually but produces a different fitted line.
Wrong regression type. A previous Exp or 1-V selection is remembered; check that LIN is active.
Reading r as r². The display is the correlation coefficient, not the coefficient of determination. Squaring r gives r² if the question asks for it.
Forecasting outside the data range. Y' extrapolates happily beyond your observations; the math works, but the assumption may not.