Two-Variable Statistics Calculator
Data =
Results
Occurrences =
X Results
Mean X =
Sum X =
Sum X² =
Std Dev X [sample] =
Std Dev X [pop] =
Variance X [sample] =
Variance X [pop] =
Minimum X =
Maximum X =
Range X =
Y Results
Mean Y =
Sum Y =
Sum Y² =
Std Dev Y [sample] =
Std Dev Y [pop] =
Variance Y [sample] =
Variance Y [pop] =
Minimum Y =
Maximum Y =
Range Y =
Sum XY =
Regression
Method = 1
A =
B =
r =
r² =
Predicted
Predicted X =
Predicted Y =
regression_data =
Help
Calculates descriptive statistics for two-variable data sets (variables x and y) with equal numbers of observations. Data includes mean, occurrences, sums, standard deviations, variances, minimums and maximums. It also calculates linear, natural log, log, exponential and power regressions with prediction capabilities.
Each data point should be entered on a row in the form x;y. See Examples for more.
Rows
Two-Variable Statistics
- Data: Data set in the form x; y (one point by row).
Results
- Occurrences: Number of rows.
- Mean X: Mean of x values.
- Sum X: Sum of x values.
- Sum X²: Sum of squared x values.
- Std Dev X [sample]: Sample standard deviation of x values (commonly denoted s).
- Std Dev X [pop]: Population standard deviation of x values (commonly denoted sigma).
- Variance X [sample]: Sample variance of x values (commonly denoted s²).
- Variance X [pop]: Population variance of x values (commonly denoted sigma²).
- Minimum X: Minimum x value.
- Maximum X: Maximum x value.
- Range X: Difference between x minimum and maximum values.
- Mean Y: Mean of y values.
- Sum Y: Sum of y values.
- Sum Y²: Sample standard deviation of y values (commonly denoted s).
- Std Dev Y [sample]: Sample standard deviation of y values (commonly denoted s).
- Std Dev Y [pop]: Population standard deviation of y values (commonly denoted sigma).
- Variance Y [sample]: Sample variance of y values (commonly denoted s²).
- Variance Y [pop]: Population variance of y values (commonly denoted sigma²).
- Minimum Y: Minimum y value.
- Maximum Y: Maximum y value.
- Range Y: Difference between minimum and maximum y values.
- Sum XY: Sum of x times y values.
- Method: Regression method. Regression (curve fitting) works best with as much data as possible. See below for regression equations used for each regression method.
- A: A Regression coefficient in the formulas below.
- B: B Regression coefficient in the formulas below.
- r: Simple correlation coefficient.
- r²: Coefficient of determination.
- Predicted X: Predicted x-value.
- Predicted Y: Predicted y-value.
Regression Equations
- Linear: y = A*x + B
- Natural Log: y = A + B * ln(x) for x > 0
- Logarithm: y = A + B * log(x) for x > 0
- Exponential: y = A*B^x
- Power: y = A*x^B
Examples
Your company has five sales offices around the world and is thinking of adding a sixth. The president of the company wants to know if there is a correlation between the number of salespersons at a branch and the volume of sales per month. What volume of sales can be expected at the new sixth branch if it has 10 sales people? (Data for other branches is below, listed as sales employees;dollar sales.)
- Data:
8; 2,000,000
13; 2,372,500
15; 3,975,000
18; 4,275,900
12; 2,428,200
This calculates our summary data.
- Method: Linear
- Predicted X: 10
We can see our Predicted Y (sales) for the new branch is $2,199,167. We can also see that the number of salesperson’s affects revenue. This is known because the correlation coefficient r is 0.91 (the closer to 1 or –1 the better).
Keywords
Data
Occurrences
Mean X
Sum X
Sum X²
Std Dev X [sample]
Std Dev X [pop]
Variance X [sample]
Variance X [pop]
Minimum X
Maximum X
Range X
Mean Y
Sum Y
Sum Y²
Std Dev Y [sample]
Std Dev Y [pop]
Variance Y [sample]
Variance Y [pop]
Minimum Y
Maximum Y
Range Y
Sum XY
Method
A
B
r
r²
Predicted X
Predicted Y
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2-Variable
2 Variable
Two Variable
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