HP 15c Manual

 Section 4: Statistics Functions 51 
 
X NITROGEN APPLIED 0.00 20.00 40.00 60.00 80.00 (kg per hectare *), x 
Y 
GRAIN YIELD 
4.63 4.78 6.61 7.21 7.78 (metric tons per 
hectare), y 
*A hectare equals 2.47 acres. 
Keystrokes Display  
´ CLEAR ∑ 0.0000 Clears statistical storage registers (R2 through R7 and the stack). 
´ • 2 0.00 Limits display to two decimal places, like the data. 
4.63 v 4.63  
0 z 1.00 First data point. 
4.78 v 4.78  
20 z 2.00 Second data point. 
6.61v 6.16  
40 z 3.00 Third data...

52 Section 4: Statistics Functions 
 
Correcting Accumulated Statistics 
If  you  discover  that  you  have  entered  data  incorrectly,  the  accumulated 
statistics  can  be  easily  corrected.  Even  if  only  one  value  of  an  (x,  y)  data 
pair is incorrect, you must delete and re-enter both values. 
1. Key the incorrect data pair into the Y- and X-register. 
2. Press |w to delete the incorrect data. 
3. Key in the correct values for x and y. 
4. Press z. 
Alternatively,  if  the  incorrect  data...

 Section 4: Statistics Functions 53 
 
Mean 
The ’ function  computes  the  arithmetic  mean  (average)  of  the x-and y-
values  using  the  formulas  shown  in  appendix  A  and  the  statistics 
accumulated in the relevant registers. When you press |’ the contents 
of the stack lift (two registers if stack lift is enabled, one if not); the mean of 
x ( x)  is  copied into  the  X-register  as  the  mean  of y ( y)  is  copied 
simultaneously into the Y-register. Press ® to view  y. 
Example: From  the...

54 Section 4: Statistics Functions 
 
Example: Calculate  the  standard  deviation  about  the  mean  calculated 
above. 
Keystrokes Display  
|S 31.62 Standard deviation about the  mean  nitrogen 
application,  x. 
® 1.24 Standard  deviation  about  the  mean  grain 
yield,  y. 
Linear Regression 
Linear  regression  is  a  statistical  method  for  finding a straight  line  that  best 
fits  a  set  of  two or more  data  pairs,  thus  providing  a  relationship  between 
two or more data pairs, thus...

 Section 4: Statistics Functions 55 
 
Example: Find the y-intercept and slope of the linear approximation of the 
data and compare to the plotted data on the graph below. 
 
Keystrokes Display  
´L 4.86 y-intercept of the line. 
® 0.04 Slope of the line. 
Linear Estimation and Correlation Coefficient 
When  you press ´j the linear estimate, ŷ, is placed in the  X-register 
and  the correlation  coefficient,  r, is  placed  in  the  Y-register.  To  display r, 
press ®.   

56 Section 4: Statistics Functions 
 
Linear  Estimation. With the  statistics accumulated, an estimated value  for 
y,  denoted ŷ,  can  be  calculated  by  keying  in  a  proposed  value  for x and 
pressing ´j. 
An Estimated value for x (denoted) can be calculated as follows: 
1. Press ´L. 
2. Key in the known y-value. 
3. Press ® - ® ÷. 
Correlation  Coefficient. Both  linear  regression  and  linear  estimation 
presume  that  the  relationship  between  the x and y data  values  can  be...

 Section 4: Statistics Functions 57 
 
 
Keystrokes Display  
70 ´j 7.56 
 
Predicted grain yield in tons/hectare. 
® 0.99 The original data closely approximates a 
straight line. 
Other Applications 
Interpolation. Linear  interpolation  of  tabular  values,  such  as  in 
thermodynamics and statistics tables,  can be  carried out  very  simply on the 
HP-15C  by  using  the j function.  This  is  because  linear  interpolation  is 
linear  estimation:  two  consecutive  tabular  values  are  assumed...

 
58 
Section 5 
The Display 
and Continuous Memory 
Display Control 
The  HP-15C  has  three  display  formats – •, i, and ^  – that 
use a given number (0 through 9) to specify display format. The illustration 
below shows how the number 123,456 would be displayed specified to four 
places in each possible mode. 
´ • 4 : 123,456.0000 
´ i 4 : 1.2346    05 
´ ^ 4 : 123.46    03 
Owing to Continuous Memory, any change you make in the display format 
will be preserved until Continuous Memory is reset....

 Section 5: The Display and Continuous Memory 59 
 
 
Scientific Notation Display 
i (scientific) format  displays  a  number  in  scientific  notation.  The 
sequence ´i n specifies the  number of decimal  places to be  shown. 
Up  to  six  decimal  places  can  be shown  since  the  exponent display  takes 
three  spaces.  The  display  will  be  rounded  to  the  specified  number  of 
decimal  places;  however,  if  you  specify  more  decimal  places  than  the  six 
places the display can hold...

60 Section 5: The Display and Continuous Memory 
 
Mantissa Display 
Regardless  of  the  display  format,  the  HP-15C  always  internally  holds  each 
number as a 10-digit mantissa and a two-digit exponent of 10. For example, 
π  is  always  represented  internally  as  3.141592654×1000,  regardless  of  what 
is in the display. 
When  you  want  to  view  the  full  10-digit  mantissa  of  a  number  in  the  X-
register,  press ´ CLEAR u.  To  keep  the  mantissa  in  the  display, 
hold the u key...