E-18
To calculate the linear regression and logarithmic regression
correlation coefficients for the following paired-variable data and
determine the regression formula for the strongest correlation: (
x, y)
= (20, 3150), (110, 7310), (200, 8800), (290, 9310). Specify Fix 3
(three decimal places) for results.
(SETUP)A(STAT)(OFF)
(SETUP)(Fix)
(STAT)(A+BX)
20 110 200 290 AC
3150 7310 8800 9310
(STAT)(Reg)(r)
(STAT)(Type)(In X)
(STAT)(Reg)(r)
(STAT)(Reg)(A)
(STAT)(Reg)(B)
Results: Linear Regression Correlation Coefficient: 0.923
Logarithmic Regression Correlation Coefficient: 0.998
Logarithmic Regression Formula:
y = –3857.984 + 2357.532lnx
Calculating Estimated Values
Based on the regression formula obtained by paired-variable statistical
calculation, the estimated value of
y can be calculated for a given x-value.
The corresponding
x-value (two values, x
1
and x
2
, in the case of quadratic
regression) also can be calculated for a value of
y in the regression
formula.
To determine the estimate value for y when x = 160 in the
regression formula produced by logarithmic regression of the data
in
3
. Specify Fix 3 for the result. (Perform the following operation
after completing the operations in
3
.)
160 (STAT)(Reg)(L)
Result: 8106.898
Important: Regression coefficient, correlation coefficient, and estimated
value calculations can take considerable time when there are a large number
of data items.
Calculation Ranges, Number of Digits,
and Precision
The calculation range, number of digits used for internal calculation, and
calculation precision depend on the type of calculation you are performing.
Calculation Range and Precision
Calculation Range
p1 s 10
–99
to p9.999999999 s 10
99
or 0
Number of Digits for Internal
Calculation
15 digits
33
STAT
FIX
STAT
FIX
44
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