Linear Regression with Vector Data on Windows

Create the Paired Data

Use one vector for x-values and a second vector for the corresponding y-values. In this example, x contains the values 1 through 5 and y contains five measured or observed values:

vector(1,2,3,4,5)
vector(2,4,5,4,5)

The entries pair by position: (1,2), (2,4), (3,5), (4,4), and (5,5). The two vectors must have matching lengths and contain real numeric data for the supported paired-data workflow.

Calculate Correlation

Pass two vectors to the supported Pearson correlation function:

correlation(vector(1,2,3,4,5), vector(2,4,5,4,5))

Correlation measures the direction and strength of linear association. A positive value indicates that larger x-values tend to occur with larger y-values in this sample. It does not prove causation and does not by itself tell you whether a linear model is appropriate for a consequential decision.

Calculate the Fitted Line

Use the same paired vectors with the linear-regression function:

linear_regression(vector(1,2,3,4,5), vector(2,4,5,4,5))

For supported paired data, linear_regression(...) returns a 1-by-2 row matrix in the form [slope, intercept]. The slope estimates how much fitted y changes for each one-unit increase in x. The intercept is the fitted y-value at x equal to zero, even if zero lies outside the observed data range.

Graph the Points and Regression Line

Now ask SumWise to prepare the regression plot:

graph_regression(vector(1,2,3,4,5), vector(2,4,5,4,5))

The current verified public screenshot reports:

Points: 5
Slope: 0.6
Intercept: 2.2
Correlation: 0.774597
R^2: 0.6
Regression line: y = 0.6*x + 2.2

The positive slope matches the visible upward direction of the fitted line. The correlation is positive but below 1 because the points do not fall perfectly on a straight line. R-squared is a basic fit summary; the displayed value of 0.6 should be interpreted in the context of this small example rather than as a universal model-quality threshold.

Inspect the Visual Result

Compare each plotted point with the fitted line. The point at (3,5) lies above the line, while (4,4) lies below it. Those deviations are part of why the fit is not perfect. The graph is useful for checking the overall pattern and spotting observations that deserve attention before relying on a summary alone.

Use the visible zoom, pan, and reset controls when you need a closer view. The graph can also be copied as an image or exported as PNG for notes and teaching material.

Add Descriptive Context

You can reuse either vector with supported descriptive functions. For example:

mean(vector(2,4,5,4,5))
standard_deviation(vector(2,4,5,4,5))

These calculations describe the y-values themselves, while correlation and regression describe the relationship between x and y. Keeping them in one history helps maintain the connection between the data and the summaries you calculate.

Current Scope and Responsible Use

SumWise supports descriptive statistics, Pearson correlation, introductory paired-data linear regression, scatter plots, and regression plots. It is not a full statistical-analysis environment and does not claim multiple regression, hypothesis testing, ANOVA, time-series modeling, or automatic model validation. Check important results with appropriate statistical methods and professional judgment.

Once SumWise is installed, these calculations and graph preparation are designed to run locally. Microsoft Store manages installation, the trial, purchase, and license verification.

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