HP 35s User Manual

							 
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HP 35s  Trend Lines 
 
hp calculators - 5 - HP 35s  Trend Lines - Version 1.0 
 Figure 13 
 
 To estimate sales for the second quarter of next year (quarter 10), do the following: 
 
 In either RPN or algebraic mode, press: 2+-#$& 
 
 Figure 14 
  
 To estimate sales for the third quarter of the next year (quarter 11), do the following: 
 
 In either RPN or algebraic mode, press: 2++#$& 
 
 Figure 15   
						

							 
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HP 35s  Trend Lines 
 
hp calculators - 6 - HP 35s  Trend Lines - Version 1.0 
 To estimate sales for the fourth quarter of next year (quarter 12), do the following: 
 
 In either RPN or algebraic mode, press: 2+/$& 
 
 Figure 16 
 
 To estimate the month during which sales would reach $38,000, do the following: 
 
 In either RPN or algebraic mode, press: 203---$ 
 
 Figure 17 
 
Answer: Sales for quarters 9 through 12 are predicted to be $33,907, $34,351, $34,796 and $35,241. Sales are  
 predicted to reach $38,000 between months 18 and 19. The correlation is 0.90, which indicates a fairly  
 strong relationship and predictive ability. 
   
						

							 
 
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HP 35s  Cost Estimation using Linear Regression 
 
 
 
 
Cost estimation using Linear Regression 
 
Practice estimating costs using linear regression 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Cost Estimation using Linear Regression 
 
hp calculators - 2 - HP 35s  Cost Estimation using Linear Regression - Version 1.0 
Cost estimation using Linear Regression 
 
Linear regression calculates the equation for a line that best fits a set of ordered pairs by minimizing the sum of the 
squared residuals between the actual data points and the predicted data points using the estimated line’s slope and 
intercept. The equation of the line produced by linear regression is in the form Y = mX + b, where m is the slope of the 
line and b is the Y-intercept. Once the slope and intercept have been calculated, it is fairly easy to substitute other values 
for X and predict a corresponding value for Y, or to substitute a value for Y and predict a value for X. When the X value is 
a measure of time (months or years, for example), the equation is specifically referred to as a trend line.  
 
Linear regression is often used to estimate the fixed and variable components from a company’s or department’s total 
costs. In these circumstances, the values for X are usually the cost driver for the organization or department. Examples 
might include units produced, hours worked, hours of machine time, and others. The values for Y are the total cost for 
that level of X input. The computed slope of the linear regression line will indicate the variable cost per unit of X, while 
the computed Y-intercept will indicate the fixed cost.  
 
In many or most circumstances, this type of cost analysis will generate slopes and Y-intercepts that make sense in the 
real world. It is sometimes possible, though, that the fixed cost component in particular may not make any sense. The 
generated Y-intercept (fixed cost) might be negative, for example, to make the linear regression line fit the observed cost 
data as closely as possible. Be aware, as well, that it is rarely a good idea to use such an equation to predict too far 
away from the range of the actual data used, since circumstances can change rather quickly. In other words, if you fit a 
line using cost data for units produced from 500 to 1,500 a month, making cost predictions using forecasted production 
levels of 5,000 units a month may generate unreliable results. Also, since time is not a variable in these calculations, the 
order in which the costs are input as data points does not matter – you may enter the data points in any order desired. 
 
On the HP 35s, values are entered into the statistical / summation registers by keying in the number (or pair of numbers) 
desired and pressing !. This process is repeated for all numbers or pair of numbers.  When entering a pair of 
numbers in RPN or algebraic mode, key the Y value, press , then key the X value and press !.  
 
To view the linear regression results, press #$. The HP 35s displays a menu of relevant values. Items on this 
menu are viewed by pressing the % or & cursor keys of the HP 35s. 
 
This menu allows you to predict a value for X given a Y value, or predict a value for Y given an X value. It also displays 
the linear regression lines correlation, slope, and y-intercept. The correlation will always be between –1 and +1, where 
values closer to –1 and +1 indicating a good “fit” of the line to the data. Values nearer to zero indicate little to no “fit.” 
Little reliance should be placed upon predictions made where the correlation is not near –1 or +1. Exactly how far away 
from these values the correlation can be and the equation still be considered a good predictor is a matter of debate. To 
use a value displayed on the menu, press the  button and the value will be copied for further use. This is 
illustrated in the problems below.   
						

							 
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HP 35s  Cost Estimation using Linear Regression 
 
hp calculators - 3 - HP 35s  Cost Estimation using Linear Regression - Version 1.0 
Practice estimating costs using linear regression 
 
Example 1: Johnson’s Chair Company has experienced the following costs for the first 6 months of the year: 
 
 # Chairs Made  Total Costs 
 5,000 $120,000 
 5,500 $122,100 
 4,800 $118,540 
 5,300 $122,400 
 4,950 $119,100 
 5,150 $124,200 
 
 What estimate would a linear regression equation produce for Johnson’s fixed and variable cost? How  
 good is the fit of the linear regression line generated (What is the correlation)? What are the total costs  
 predicted if 5,400 chairs were to be made? If the total costs were $125,000, how many chairs would you  
 estimate had been produced?  
  
Solution: The X values will be the number of chairs produced. The Y values will be the total costs. Be sure to clear  
 the statistics / summation memories before starting the problem.  
 () 
 
 In RPN or algebraic mode, press: 
 
*+,----.---!*
*+,,+--..--!*
*++/.)-)/--!*
*+,,)--.0--!*
*++1+--)1.-!*
*+,),--.+.-!*
 
 To view the linear regression results, press #$. Figure 2 displays the menu shown. 
 
 Figure 2 
 
 In either RPN or algebraic mode, press: &&& to view the slope. 
 
 Figure 3 
 
 In either RPN or algebraic mode, press: & to view the y-intercept. 
   
						

							 
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HP 35s  Cost Estimation using Linear Regression 
 
hp calculators - 4 - HP 35s  Cost Estimation using Linear Regression - Version 1.0 
 Figure 4 
 
 In either RPN or algebraic mode, press: %% to view the correlation. 
 
 Figure 5 
 
 To estimate costs if 5,400 chairs are made, do the following: 
 
 In either RPN or algebraic mode, press: 2.)--#$& 
 
 Figure 6 
 
 To estimate the number of chairs made if the costs were $125,000, do the following: 
 
 In either RPN or algebraic mode, press: 2+,.---#$ 
 
 Figure 7 
 
Answer: The linear regression equation generated is of the form: Y = 6.18X + 89449.38. The slope of 6.18 is the  
 estimate for the variable cost and the Y-intercept of 89,449.38 is the estimate for the fixed cost. The  
 correlation value of 0.72 is not as close to +1 as might be hoped, but still indicates a moderate fit. The total  
 cost estimate if 5,400 chairs were made is $122,806. The estimated number of chairs made if the total  
 costs were $125,000 is 5,755 chairs. 
 
Example 2: The stamping department cost analyst is reviewing the total cost compared with the number of machine  
 hours used for the last 4 weeks. 
  
 # Machine Hours Total Costs 
 350 $55,000 
 375 $57,300 
 400 $58,100 
 360 $56,250 
 
 What estimate would a linear regression equation produce for the stamping department’s fixed and variable  
 cost? How good is the fit of the linear regression line generated (What is the correlation)? What are the  
 total costs predicted if 380 machine hours are used next week? If the total costs were $60,000, how many  
 machine hours would you estimate had been used?    
						

							 
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HP 35s  Cost Estimation using Linear Regression 
 
hp calculators - 5 - HP 35s  Cost Estimation using Linear Regression - Version 1.0 
Solution: The X values will be the number of machine hours used. The Y values will be the total costs. Be sure  
 to clear the statistics / summation memories before starting the problem.  
 () 
 
 In RPN or algebraic mode, press: 
 
*..---0.-!*
*.30--03.!*
*./+--)--!*
*.4,.-04-!*
 
 To view the linear regression results, press #$. Figure 8 displays the menu shown. 
 
 Figure 8 
  
 In either RPN or algebraic mode, press: &&&to view the slope. 
 
 Figure 9 
 
 In either RPN or algebraic mode, press: & to view the y-intercept. 
 
 Figure 10 
 
 In either RPN or algebraic mode, press: %% to view the correlation. 
 
 Figure 11 
 
 To estimate costs if 380 machine hours are used, do the following: 
 
 In either RPN or algebraic mode, press: 20/-#$& 
 
 Figure 12   
						

							 
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HP 35s  Cost Estimation using Linear Regression 
 
hp calculators - 6 - HP 35s  Cost Estimation using Linear Regression - Version 1.0 
 To estimate the number of number of machine hours used if costs were $60,000, do the following: 
 
 In either RPN or algebraic mode, press: 24----#$ 
 
 Figure 13 
 
Answer: The linear regression equation generated is of the form: Y = 58.99X + 34,763.66. The slope of 58.99 is  
 the estimate for the variable cost per machine hour and the Y-intercept of 34,763.66 is the estimate for  
 the fixed cost. The correlation value of 0.96 is quite close to +1 and indicates a very good fit. The total  
 cost estimate if 380 machine hours are used is $57,178. The estimated number of machine hours used  
 if the total costs were $60,000 is 427.8 machine hours.   
						

							 
 
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HP 35s  Percentages and Percentage Changes 
 
 
 
 
 
Percentages 
 
Practice working problems involving percentages 
 
Practice working problems involving  
percentage changes 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
   
						

							 
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HP 35s  Percentages and Percentage Changes 
 
hp calculators - 2 - HP 35s  Percentages and Percentage Changes - Version 1.0 
Percentages 
 
A percentage is a fraction multiplied by 100. For example, 25 percent is written 25%, and is 0.25 (one quarter) multiplied 
by 100. 
 
Percentages are used very widely in business, for example to specify bank rate, interest rates, tax rates, or discounts. 
Percentages and percent changes are also used outside business –  scientific or engineering measurements, results, 
and uncertainties are stated as percentages. 
 
The HP 35s provides a % key for use in calculating percentages, and adding or subtracting percentages. It also provides 
a percent change key for the calculation of changes as percentages. 
 
Practice working problems involving percentages 
 
Most business calculations are made to the nearest cent or penny, so it is useful to set the display mode of the HP 35s 
to FIX 2 before doing these practice problems, to have two digits displayed after the decimal point. Press 
!#$ to set FIX  2 mode. 
 
Example 1: What is 12% of $1,235.17? 
 
Solution: In RPN mode, the number 1,235.17 is typed and then % is pressed. Then 12 is typed and the & 
key is pressed. 
 
 #$()#*%#$+&,
 
 Figure 1 
 
 The number 1,235.17 is still displayed in the upper line (it is left in register Y) and the result, 12% of 
1,235.17, is displayed in the lower line (in register X). Unlike other RPN commands such as - or ., the 
& command leaves the number in the Y register unchanged. This makes it possible to continue a 
calculation, using that number. This will be shown in the next example. 
 
 In algebraic mode, press: 
 
 +&#$()#*/#$% 
 
 
 Figure 2 
 
 Note that in algebraic mode “n” percent of something is obtained by multiplying by the percentage. 
 
Answer: 12% of $1,235.17 is $148.22 when written to the nearest cent.