Introduction to regression analysis formula:
In mathematics, one of the most important topics in statistics is regression. Regression analysis formula is determining the relationship between two variables. Regression analysis formula are used to analysis the several variables. Regression is one of the statistical analysis methods that can be used to assessing the association between the two different variables. Here we are going to discuss about regression analysis formula with suitable example problems.
Formula for Regression Analysis:
Here we study about calculate the regression analysis formulas are,
Formula for regression analysis:
Regression Equation (y) = a + bx
Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`
Intercept `(a) = (sumY-b(sumX))/N`
Where,
x and y are the variables.
b = the slope of the regression line is also defined as regression coefficient
a = intercept point of the regression line where is in the y-axis.
N = Number of values or elements
X = First Score
Y = Second Score
`(sumXY)` = Sum of the product of the first scores and Second Scores
`(sumX)` = Sum of First Scores
`(sumY)` = Sum of Second Scores
`(sumX^2)` = Sum of square First Scores.
Example Problem for Regression Analysis Formula:
Problem for regression analysis formula:
Example 1:
Find the regression slope coefficient, intercept value and create a regression equation by using the given table.
In mathematics, one of the most important topics in statistics is regression. Regression analysis formula is determining the relationship between two variables. Regression analysis formula are used to analysis the several variables. Regression is one of the statistical analysis methods that can be used to assessing the association between the two different variables. Here we are going to discuss about regression analysis formula with suitable example problems.
Formula for Regression Analysis:
Here we study about calculate the regression analysis formulas are,
Formula for regression analysis:
Regression Equation (y) = a + bx
Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`
Intercept `(a) = (sumY-b(sumX))/N`
Where,
x and y are the variables.
b = the slope of the regression line is also defined as regression coefficient
a = intercept point of the regression line where is in the y-axis.
N = Number of values or elements
X = First Score
Y = Second Score
`(sumXY)` = Sum of the product of the first scores and Second Scores
`(sumX)` = Sum of First Scores
`(sumY)` = Sum of Second Scores
`(sumX^2)` = Sum of square First Scores.
Example Problem for Regression Analysis Formula:
Problem for regression analysis formula:
Example 1:
Find the regression slope coefficient, intercept value and create a regression equation by using the given table.
| X Values | Y Values |
| 5 | 8 |
| 10 | 16 |
| 15 | 24 |
| 20 | 32 |
| 30 | 40 |
For the given data set of data, solve the regression slope and intercept values.
Solution:
Let us count the number of values.
N = 5
Determine the values for XY, X2
| X Value | Y Value | X*Y | X*X |
| 5 | 8 | 40 | 25 |
| 10 | 16 | 160 | 100 |
| 15 | 24 | 360 | 225 |
| 20 | 32 | 640 | 400 |
| 30 | 40 | 1200 | 900 |
| `(sumX = 80)` | `(sumY = 120)` | `(sumXY)= 2400` | `(sumX^2) = 1650` |
`(sumX) = 80`
`(sumY)= 120`
`(sumXY)= 2400`
`(sumX^2) = 1650`
Plug values in the slope formula,
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Slope `(b) = (NsumXY-(sumX)(sumY))/(NsumX^2-(NsumX)^2)`
`= (5 xx(2400)-(80)xx(120))/((5)xx(1650)-(80)^2)`
`= (12000 - 9600)/(8250-6400)`
`= 2400/1850`
`b= 1.28`
Plug the values in the intercept formula,
Intercept `(a) = (sumY- b(sumX))/N`
`= (120-(1.28xx80))/5`
`= (120 - 103.78)/5`
`= 16.22/5`
`a = 3.24`
Plug the Regression coefficient values and intercept values in the regression equation,
Regression Equation(y) = a + bx
= 3.244 + 1.28x
Answer:
Slope (or) Regression coefficient (b) = 1.28
Intercept (y) = 3.24
Regression equation y = 3.24 + 1.28x
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