The Least-squares Trend Line calculator computes the regression line, a linear equation, through a set of X and Y values. This is also known as simple linear regression. The Least-square Equation produces this linear equation in the form y = a + bx. 
INSTRUCTIONS: Enter the following:
- (X,Y) Tabular Data of X,Y pairs
Least-squares Trend Line (Y = a + bX): The calculator computes the Least-square Trend Line, correlation coefficient (r) and supporting calculations:
- (n) Number of Pairs
- (MX) Mean of X values
- (MY) Mean of Y values
- (ΣX) Sum of X values
- (ΣY) Sum of Y values
- (ΣXY) Sum of X⋅Y values
- (ΣX2) Sum of X2 values
- (ΣY2) Sum of Y2 values
Example in Graphic
If you want the find the least squares trend line through
INPUTS
1,5
2,4
3,6
4,8
5,7
The calculator will return "Y = 3.6 + 0.8X".
The Math / Science
The formula for the least-squared regression line is in the following form:
y = a + bx
where:
`b = ( (sum(XY) - (sumX * sumY)"/n")) / (sum(X^2) - (sumX)^2"/n") `
and
` a = MY - b*MX` MY is mean of Y. MX is mean of X.
Correlation
To determine if there is a correlation between X and Y, the calculator computes the correlation coefficient (r). The range of r is -1 ≤ r ≤ 1, with the strongest correlations the further one gets from zero, either negative or positive. The formula for the correlation coefficient (r) is as follows:
`r = b * (sum(X^2)- sum(X)^2"/n")/(sum(Y^2)- sum(Y)^2"/n")`
Statistics Calculators
- Observational Stats: This function accepts a table of numbers separated by commas and calculates observational statistics for any of the columns. This includes count, min, max, sum, sum of squares (Σx²), square of the sum (Σx)², mean, median, mode, range, mid point, rand, sort up, sort down, rand, population variance, population standard deviation, the sample/experimental variance, sample/experimental standard deviation.
- Frequency Distribution: This function lets you enter a string of numbers separated by commas, a low and high range and a number of bins. It then computes how many of the observations are in each of the bins between the high and low values designated.
- Paired Sample t-test: This computes the various parameters associated with the Paired Sample t-test.
- ANOVA (one way): The is one way analysis of variance
- (χ2) Chi-Square Test: This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.
- Linear Regression: This computes the regression line (least-squares) through a set of X and Y observations. It also computes the regression coefficient (r).
- y = a + bx: This is linear equation used with Linear Regression to predict values of Y.
- Wilcoxon Signed Rank Test: This provides the Wilcoxon statistics and critical value for two groups of numeric observations based on an alpha value and whether it's a one or two tailed test.
- Slope-Intercept form of a Line based on two points.
- Slope between two points
- Range value based on the slope-intercept formula of a line and a value of the domain.
- Compute the Probability between z SCORES
- College Level Statistics Calculator (Stat Calc).
- Count of Observations in a Set - this is the number (n) of values in a set.
- Minimum Value in a Set - this is the minimum observed value
- Maximum Value in a Set- this is the maximum value in the set.
- Numeric Sort (up and down) - this returns a comma separated list of the observations in ascending or descending order.
- Create a random subset of the a list of numeric values
- Random number from a range you specify
- Frequency distribution of data.
- Σx - this is the sum of the values in a set.
- Σx² - this is the sum of the squared values
- (Σx)² - this is the square of the summed values.
- Mean - the is the mean (average) of the observed values
- Median - the middle ordered value
- Mode - the most recurring observation
- Mid Point in a Set - this is the mid point of the observation range.
- Range in a Set - this is the difference between the max and the min.
- Population Variance of the values
- Population standard deviation of the values
- Sample Variance of the values
- Sample Standard Deviation of the values
- Compute the z SCORE based on the mean and standard deviation
- Compute the z SCORE in a set of observations
- Compute the percentile of a single observation (y) in a set (X)
- SDOM - standard deviation of mean
- Percent Relative Standard Deviation
References
- Dowdy, Shirley, and Stanley Wearden. Statistics for Research. N.p.: John Wiley & Sons, n.d. Print.(Chapter 9 Distributions of Paired Variables)