How to Find Regression Equation?

A simple linear regression is a method in statistics which is used to determine the relationship between two continuous variables. A simple linear regression fits a straight line through the set of n points. Learn here the definition, formula and calculation of simple linear regression. Check out this simple/linear regression tutorial and examples here to learn how to find regression equation and relationship between two variables. using the slope and y-intercept.

Simple / Linear Regression Tutorial, Examples

Regression Definition:

A regression is a statistical analysis assessing the association between two variables. In simple linear regression, a single independent variable is used to predict the value of a dependent variable.

Regression Formula:

Regression Equation(y) = a + bx Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) Intercept(a) = (ΣY - b(ΣX)) / N Where, x and y are the variables. b = The slope of the regression line a = The intercept point of the regression line and the y axis. N = Number of values or elements X = First Score Y = Second Score ΣXY = Sum of the product of first and Second Scores ΣX = Sum of First Scores ΣY = Sum of Second Scores ΣX2 = Sum of square First Scores
Regression Example:

To find the Simple/Linear Regression of

X ValuesY Values
603.1
613.6
623.8
634
654.1

To find regression equation, we will first find slope, intercept and use it to form regression equation.

Step 1:

Count the number of values. N = 5

Step 2:

Find XY, X2 See the below table

X ValueY ValueX*YX*X
603.1 60 * 3.1 =186 60 * 60 = 3600
613.661 * 3.6 = 219.661 * 61 = 3721
623.862 * 3.8 = 235.662 * 62 = 3844
63463 * 4 = 25263 * 63 = 3969
654.165 * 4.1 = 266.565 * 65 = 4225
Step 3:

Find ΣX, ΣY, ΣXY, ΣX2. ΣX = 311 ΣY = 18.6 ΣXY = 1159.7 ΣX2 = 19359

Step 4:

Substitute in the above slope formula given. Slope(b) = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2) = ((5)*(1159.7)-(311)*(18.6))/((5)*(19359)-(311)2) = (5798.5 - 5784.6)/(96795 - 96721) = 13.9/74 = 0.18784

Step 5:

Now, again substitute in the above intercept formula given. Intercept(a) = (ΣY - b(ΣX)) / N = (18.6 - 0.18784(311))/5 = (18.6 - 58.41824)/5 = -39.81824/5 = -7.964

Step 6:

Then substitute these values in regression equation formula Regression Equation(y) = a + bx = -7.964+0.188x.
Suppose if we want to know the approximate y value for the variable x = 64. Then we can substitute the value in the above equation. Regression Equation(y) = a + bx = -7.964+0.188(64). = -7.964+12.032. = 4.068 This example will guide you to find the relationship between two variables by calculating the Regression from the above steps.

This tutorial will help you dynamically to find the Simple/Linear Regression problems.

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