Regression Slope Coefficient

Introduction to regression slope coefficient:
In mathematics, regression is one of the interesting topics in statistics. Linear regression is defined as the process of determining the relationship between two variables. It is a statistical analysis method which can be used to assessing the association between the two different variables. Let us see some example problems using regression slope coefficient.

Regression Slope Coefficient - Formula for Regression:

Formula for Regression:

Regression Equation (y) = a + bx
Regression Slope coefficient  (b) = `(NsumXY - (sumX) (sumY)) / (NsumX^2 - (sumX)^2)`
Intercept(a) =`(sumY - b(sumX)) / N `

Where
x and y are the variables.
b = the slope of the regression line (also called as regression slope coefficient)
a = the intercept point of the regression line and in the y-axis.
N = Number of values or elements
X = First Score
Y = Second Score
`sumXY` = Sum for the product of the first and Second Scores
`sumX` = Sum of First Scores
`sumY` = Sum of Second Scores
`sumX^2` = Sum of square First Scores. I like to share this Adding and Subtracting Significant Figures with you all through my article.

Regression Slope Coefficient - Example Problem:

Example 1:

Find the regression equation by using the regression slope coefficient value.

For the given data set of data, solve the regression slope coefficient.
Solution:

Let us count the number of values.
N = 6

Determine the values for XY, X2

Determine the following values `sumX` , `sumY` , `sumXY` , `sumX^2` .
`sumX` = 444
`sumY` = 21.4
`sumXY` = 1589.1
`sumX^2` = 32890

Substitute values in the slope formula
Regression Slope coefficient (b) = `(NsumXY - (sumX) (sumY)) / (NsumX^2 - (sumX)^2)`
= `((6)*(1589.1)-(444)*(21.4))/((6)*(32890)-(444)^2)`
= `(9534.6 - 9506.1)/ (197340 - 197136)`
=`28.5/204`
= 0.14
Substitute the values in the intercept formula given.
Intercept (a) = `(sumY - b (sumX)) / N `
=` (21.4 - 0.14(444))/6`
= `(21.4 - 62.16)/6`
= -`40.76/6`

= -6.79

Substitute the Regression coefficient and intercept values in the regression equation
Regression Equation(y) = a + bx
= -6.79 + 0.14x.

Solution:

Regression Slope coefficient (b) = 0.14

Intercept (y) = - 6.79

Regression equation y = - 6.79 + 0.14x.

Determine the approximate value for y:

When x = 75

Substitute the x value into the regression equation

Regression Equation(y) = a + bx
= - 6.79 + 0.14x.

= - 6.79 + 0.14(75)

= - 6.79 + 10.5
y = 3.71

Solution:

y = 3.71