Processing...

`y = "a" + "b" * x `

Enter a value for all fields

The **Least-squares Trend Inference** calculator computes the value of the dependent variable (**Y**) based on the intercept (**a**), the slope (**b**) and a value of **X**. This is the result of a least-squares trend linear equation, through a set of X and Y values. This is also known as simple linear regression.

**INSTRUCTIONS:** Enter the following:

- (
**a**) Y axis Intercept - (
**b**) Slope of Line - (
**x**) Independent Variable

**Domain (Y):** The calculator returns the value of Y.

The formula for the least-squared regression line is in the following form:

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.

To compute the least squares trend line for a set of values, CLICK HERE.

After you have entered the values in the calculator for a, b and x, the plot function will let you enter a range (min and max) for x and a number of steps. When you enter the range for x and number of steps, it will generate a graph of the line graphing the values of **y** using your entered **a** and **b**, stepping through values of **x** between the range specified.

**Observational Stats**: This function accepts**a table**(rows and columns separated by commas) of numbers 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.**Simple Stats**: This is also provides a full set of observational stats, but on a**single row of numbers**separated by commas. The observational stats include 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 computes the F Score and details for one way analysis of variance for a nxm matrix of observations.**(χ**This computes the Chi-Square value for an nxm array of data and provides the degrees of freedom.^{2}) Chi-Square Test:**Linear Regression**: This computes the regression line (least-squares) through a set of X and Y observations. It also computes the regression coefficient (r).**Least-squares Trend Inference**: This is a linear equation used with Linear Regression to compute a predicted value of Y based on X.**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**: This provides the slope intercept form (y = mx+b) of a line based on two coordinates.**Slope between two points**: This provides the slope between two coordinates.**Linear Equation**: This computes the range (y) of a linear equation (y = mx +b) and includes a graphing function.**Probability between z SCORES**: This computes the area under the Normal Distribution curve between two z SCOREs which equates to the probability of an event in that range.**Stats Calc**: College level statistics calculator with a bundle including most of the functions in this list.**Count:**This computes the number (n) of observations in a set of numbers.**Minimum**: This computes the minimum (min) value in a set of numbers.**Maximum:**This computes the maximum (max) value in a set of numbers.**Numeric Sort:**This sorts (ascending or descending) a set of comma separated numerical observations.**Random Sample (k items):**The provides a random subset of a specified size (k) in a set of comma separated numerical observations.**Random Real Number in Range**: The provides a random real number between two specified real numbers (upper and lower bounds).**Radom Integer**: The provides a random integer between two specified integers (upper and lower bounds).**Frequency Distribution:**This provides a frequency distribution table for a comma separated set of numbers with a specified number of frequency bins between a lower and upper data range.**Sum (Σx):**This is computes the sum of the values in a set.**Sum of Squares (Σx²):**This computes the sum of the squared values in a set.**Sum Squared (Σx)²:**This computes the square of the summed values in a set.**Mean (μ)**: This computes is the mean (average) of values in a set.**Median:**This identifies the middle ordered value in a set of numbers.**Statistical Mode:**This identifies the most recurring observation in a set of numbers.**Mid Point**: This is identifies the mid point of the observation range in a set of numbers.**Range:**This is computes the difference between the max and the min values in a set of number.**Population Variance (σ**: This computes the variance, a metric regarding the spread of values, for a population set of numeric values.^{2})**Population Standard Deviation (σ):**This computes the standard deviation for a population set of numeric values.**Sample Variance (s**This computes the variance, a metric regarding the spread of values, for a sample set of numeric values within a greater population.^{2}) :**Sample Standard Deviation (s)**: This computes the standard deviation for a sample set of numeric values within a greater population.**z SCORE Formula**: This computes the z SCORE for a value base on the mean and standard deviation.**z SCORE:**This computes the z SCORE for a value (Raw Score) based on a set of values, and whether that set is sample or population.**Percentile:**This computes the percentile of a value (y) in a set (X) of values.**Standard Deviation of Mean (SDOM)**: This computes the standard deviation of mean, sometimes also known as the standard error of the mean (SEM), useful to helps quantify the uncertainty in the estimate of the mean.**Percent Relative Standard Deviation (%RSD):**This computes the percent relative standard deviation, also known as the coefficient of variation (CV). The %RSD is a measure of the dispersion of a probability distribution.

- Dowdy, Shirley, and Stanley Wearden. Statistics for Research. N.p.: John Wiley & Sons, n.d. Print.(Chapter 9 Distributions of Paired Variables)