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HP 20s Calculator - Linear Regression and Estimation

Introduction
Linear regression is a statistical method for finding a straight line that best fits a set of x,y-data. There must be at least two different x,y-pairs. The straight line provides a relationship between the x- and y-variables: y = mx + b, where m is the slope and b is the y-intercept.
Calculator symbol key
The procedures in this document use the following text to represent symbol keys:
Key
Description
Text Representation
Right shift key
RS
Left-shift key
LS
Clears statistical registers
CLSUM
Accumulates statistical data
SUM+
Arithmetic mean (average) of the x-values
xy
Divide
divide
Estimate of for a given value of y
xr
Estimate of for a given value of x
yr
To perform a linear regression
  1. Enter the x,y-data using the following instructions:
    1. Clear any previous contents of R4through R9 by pressing RS, then CLSUM
    2. Enter the first x-value and press INPUT. The HP 20s displays the x-value.
    3. Enter the corresponding y-value and press SUM+. The HP 20s displays the number of pairs of items (n) accumulated; in this case, "1.0000"
    4. Continue entering x,y-pairs. The n-value is incremented with each entry.
      To enter data for calculating the weighted mean, enter each data value as x, and its corresponding weight as y.
  2. Press:
    • RS, xr, LS, then SWAP (or RS, yr, LS, then SWAP) to display r, the correlation coefficient.
    • RS, then m,b to display m, the slope of the line, followed by LS, then SWAP to display b, the y-intercept.
To perform linear estimation
  1. Enter the x,y-data using the following instructions:
    1. Clear any previous contents of R4 through R9 by pressing RS, then CLSUM
    2. Enter the first x-value and press INPUT. The HP 20s displays the x-value.
    3. Enter the corresponding y-value and press SUM+. The HP 20s displays the number of pairs of items (n) accumulated; in this case, "1.0000"
    4. Continue entering x,y-pairs. The n-value is incremented with each entry.
      To enter data for calculating the weighted mean, enter each data value as x, and its corresponding weight as y.
  2. Enter the known x-value or y-value:
    • To estimate x for the given y, enter the y-value, then press RS, then xr
    • To estimate y for the given x, enter the x-value, then press RS, then yr
Example of linear regression and estimation
The rate of a certain chemical reaction depends on the initial concentration of one chemical. When the reaction is run repeatedly, varying only the initial concentration of the chemical, the following rates are observed:
Concentration X (moles per liter)
0.050
0.075
0.10
0.125
0.20
Rate Y (moles per liter)
0.0062
0.00941
0.0140
0.0146
0.023
Calculate the slope and y-intercept of the best straight line fitted to the data. Also calculate the correlation coefficient.
Keys
Display
Description
Press RS, then CLSUM
0.0000
Clears the statistical registers
Press .05, INPUT, .0062, then SUM+
1.0000
Press .075, INPUT, .00941, then SUM+
2.0000
Press .1, INPUT, .014, then SUM+
3.0000
Press .125, INPUT, .0146, then SUM+
4.0000
Press .2, INPUT, .023, then SUM+
5.0000
Enters the x, y-data
Press RS, then m,b
0.1093
Displays the slope
Press LS, then SWAP
0.0014
Displays the y-intercept. : indicates another result
Press RS, xr, LS, then SWAP
0.9890
Displays the correlation coefficient
Enter the rate of the reaction when the concentration equals 0.09 moles per liter:
Keys
Display
Description
Press .09, RS, then yr
0.0113
Calculates the estimate of y for x=0.09
What concentration is necessary for the rate to equal 0.0200?
Keys
Display
Description
Press .02, RS, then xr
0.1700
Calculates estimate of x for y=0.02
Press C
0.000
Clears the display and : annunciator

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