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`y = a + bx`

Enter a value for all fields

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 - (
**OC**) Output Choice (Trend Line, Details)

**Least-squares Trend Line (Y = a + bX):** The calculator computes the Least-square Trend Line, correlation coefficient (r) and supporting calculation details:

- (
**n**) Number of Pairs - (
**MX**) Mean of X values - (
**MY**) Mean of Y values - (
**ΣX**) Sum of X values - (
**Σ****Y**) Sum of Y values - (
**Σ****XY**) Sum of X⋅Y values - (
**ΣX**) Sum of X^{2}^{2}values - (
**ΣY**) Sum of Y^{2}^{2}values

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 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.

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")`

- Compute the Slope-Intercept form of a Line based on two points
- Compute the slope between two points
- Compute the Range value (y) based on the slope-intercept formula of a line (y = mx + b)
- Compute the Least-squares Linear Regression Equation
- Constant of Proportionality
- Constant of Inverse Proportionality

**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**(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).**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
- 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

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