Solves regression coefficient... \[a_{yx} =\frac{n \sum xy -\sum x \sum y}{n \sum x^{2} -(\sum x)^{2}}\]
Regression coefficients are used to summarize the relationship between a dependent variable and a set of predictor variables. The interpretation of a regression coefficient is that it tells you how much of an increase or decrease in the dependent variable is associated with a one unit increase in the variable of interest.
Enter datasets for variable X separated by SPACE
Enter datasets for variable Y separated by SPACE
Hit the equal sign to compute for regression coefficients
The regression coefficients are an important concept in linear regression. The calculator measures the relationship between two variables, typically represented by a linear equation. The coefficient of regression measures the change in the value of one variable when the other variable changes. It is the most commonly used techniques for investigating the relationship between two quantitative variables are correlation and linear regression
Solve regression coefficient if x samples are 5, 8, 7 and y samples are 3, 6, 15
To solve for the regression coefficient, we can follow these steps:
1. Write down the x and y sample data:
x = 5, 8, 7
y = 3, 6, 15
2. Calculate the mean of the x values and the mean of the y values:
mean(x) = (5 + 8 + 7) / 3 = 20 / 3 = 6.67
mean(y) = (3 + 6 + 15) / 3 = 24 / 3 = 8
3. Calculate the differences between each x value and the mean of x, and between each y value and the mean of y:
(x - mean(x)) = 5 - 6.67 = -1.67
(x - mean(x)) = 8 - 6.67 = 1.33
(x - mean(x)) = 7 - 6.67 = 0.33
(y - mean(y)) = 3 - 8 = -5
(y - mean(y)) = 6 - 8 = -2
(y - mean(y)) = 15 - 8 = 7
4. Calculate the product of the differences for each pair of x and y values:
(x - mean(x)) (y - mean(y)) = (-1.67) x (-5) = 8.35
(x - mean(x)) (y - mean(y)) = (1.33) x (-2) = -2.66
(x - mean(x)) (y - mean(y)) = (0.33) x (7) = 2.31
5. Calculate the sum of the products of the differences:
Sum of ((x - mean(x)) * (y - mean(y))) = 8.35 + (-2.66) + 2.31 = 8
6. Calculate the differences between each x value and the mean of x, squared:
(x - mean(x))^2 = (-1.67)^2 = 2.79
(x - mean(x))^2 = (1.33)^2 = 1.77
(x - mean(x))^2 = (0.33)^2 = 0.11
7. Calculate the sum of the squared differences:
Sum of (x - mean(x))^2 = 2.79 + 1.77 + 0.11 = 4.67
8. Calculate the regression coefficient (b):
b = Sum of ((x - mean(x)) * (y - mean(y))) / Sum of (x - mean(x))^2
b = 8 / 4.67 = 1.715
Therefore, the regression coefficient (b) for the given x and y samples is
