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Linear Regression and Estimation
Linear regression is a statistical method for finding a
straight line that bestfits 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.
Linear Regression. To do a linear regression calculation:
1. Enter the xy-data using the instructions on page 52.
2.
Press:
B (] (Er) (=] (SWAP] (or [e=] (5.r] [(«] [SWAP)) to display
r, the correlation coefficient.
B (~](mpb] to display m, the slope of the line, then [«]
to
display b, the y-intercept.
Linear Estimation. The straight line calculated by linear regression
can be used to estimate a y-value for a given x-value, or vice versa. To
do linear estimation calculations:
1. Enter the x,y-data using the instructions on page 52.
2. Enter the known x-value or y-value.
® To estimate x for the given y, enter the y-value, then press
(] o]
B To estimate y for the given x, enter the x-value, then press
(] G-
Example: Linear Regression and Estimation. The rate of a certain
chemical reaction depends on the initial concentration of one chemi-
cal. When the reaction is run repeatedly, varying only the initial
concentration of the chemical, the following rates are observed:
Concentration X
0.050
0.075
0.10
0.125
0.20
(moles perliter)
Rate Y (moles per
0.0062
0.00941
0.0140
0.0146
0.023
liter-seconds)
5: Statistical Calculations
57
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