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HP 12c Platinum Financial Calculator  Statistics  Correlation Coefficient
The correlation coefficient
Statistics can be understood as a set of tools involving the study of methods and procedures for collecting, classifying,
and analyzing data. Statistical tools also offer the means for making scientific inferences from summarized data, like
linear regression and forecasting. Both linear regression and forecasting are computed with the parameters that define a
curve (or line) that best represents the sample, given the plotted data of a twovariable sample is close enough to a
straight line that it can be represented this way. The correlation coefficient r is in the range (1 ≤ r ≤ 1) and measures
how close the sample is to a straight line. The closer the sample is to a straight line, the closer r will be to 1 and the
closer the forecasted points will be to the sample behavior.
HP 12c Platinum correlation coefficient
On the HP 12c Platinum, statistics data are stored as a set of summations resulting from the originally collected data. The
collected data set must be typed in prior to using any statistics features available in the HP 12c Platinum. The HP 12c Platinum memory
organization allows the study of statistic data organized as one or twovariable sample. As a general procedure, data is
always collected as a pair of n numbers, or (x_{n},y_{n}) values, and the HP 12c Platinum computes the following summations:
Figure : Calculating the values for x and y
With these values updated and stored in memory, the HP 12c Platinum computes the correlation coefficient with the following
expression:
Figure : Method for calculating the correlation coefficient
There are also functions to forecast values for each of the two variables. These functions are associated to (forecast
x given y) and (forecast y given x) keys. Each time a new forecast is calculated, the correlation coefficient is
computed too, and pressing right after or shows its value. The HP 12c Platinum uses the following
expressions to compute the forecasted values:
Figure : Method for calculating the forecasted values
Practice finding the correlation coefficient
Example 1
A land researcher wants to compute the relationship between the constructed area and the land area of a
community in order to suggest the construction area for a new home with a land area of 12500 sq yards
and the suggested land area for a construction with 3520 sq yards based on forecasted values. He also
wants to know how good this relationship fits in a straight line to know if his suggestions are valid. The table
below summarizes his measurements.
Land Area (sq yards)

Construction Area (sq yards)

Land Area (sq yards)

Construction Area (sq yards)

12000

3120

9000

2080

10000

2560

10000

2700

11000

2920

13000

3280

14000

3300

12000

3080

Solution
Be sure to clear the statistics/summation memories before starting the problem.
Keystroke

Display


Figure : Clearing the statistics/summation memory

Then enter the first data point.
Keystroke

Display


Figure : Entering the first data

The first entered value (construction area) is used as the y variable and the second value (land area) is
used as the x variable. The display shows the number of entries each time is pressed. Make sure that
all data is entered:
Keystroke

Display


Figure : Entering all the data

Since the yvalues are the construction area, the forecast construction area (y) for a 12500 sq yards land
area is computed by pressing:
Keystroke

Display


Figure : Calculating the forecast construction area

The correlation coefficient is automatically computed each time a forecasting is performed. Press:
Keystroke

Display


Figure : Calculating the correlation coefficient

The land area is stored as xvalues, so for a 3520 sq yards construction area, the forecasted land area is:
Keystroke

Display


Figure : Calculating the forecasted land area

Although the correlation coefficient has the same value for the same sample, it's easy to check for it:
Keystroke

Display


Figure : Calculating the correlation coefficient

Answer
For a construction area of 3,520 sq yards, the estimated land area needed is approximately 14,140 sq
yards. For a land area of 12,500 sq yards, a construction area of approximately 3,140 sq yards is
recommended. The sample shows a correlation coefficient of 0.95, so the forecast is close to the actual
data.
Example 2
A stockholder observes the foreign stock market for some time in order to compose a curve that relates the
amount of investment with amount of earnings in a particular brand. He decides to analyze the data and
use the correlation coefficient to measure the margin of error when predicting the amount of earnings given
the amount of investment. If the correlation coefficient is lower than 0.80, then he will not use the data to
make future predictions. The collected data so far is as follows:
Investment amount

Amount of earnings

Investment amount

Amount of earnings

$1,200,000

$91,000

$1,450,000

$112,000

$1,000,000

$98,000

$1,300,000

$109,000

$900,000

$85,000

$1,150,000

$99,000

Solution
Be sure to clear the statistics/summation memories before starting the problem.
Keystroke

Display


Figure : Clearing the statistics/summation memory

Consider that each pair must be entered prior to add it to the statistics summations.
Keystroke

Display


Figure : Entering the first data

Remember that the display shows the number of entries each time is pressed. Make sure that all data
is entered:
To compute the correlation coefficient, press:
Keystroke

Display


Figure : Calculating the correlation coefficient

Answer
The correlation coefficient for the collected data is 0.84, and it is higher than the stockholder defined.
Therefore, the available data will be used to predict future investments.
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