Linear Regression Equation Analysis
The equation for linear regression is given as $Y = a + bX$. This equation describes the relationship between a dependent variable ($Y$) and an independent variable ($X$).
- $Y$: Represents the dependent variable.
- $X$: Represents the independent variable.
- $a$: Represents the Y-intercept. This is the value of $Y$ when $X=0$.
- $b$: Represents the slope of the regression line.
Understanding the Regression Coefficient 'b'
The coefficient $b$ quantifies the change in the dependent variable ($Y$) for each one-unit increase in the independent variable ($X$). It is formally known as the regression coefficient or the slope.
In the context of the given equation $Y = a + bX$, the term $b$ specifically denotes the Regression coefficient.
Important Questions from Correlation and Regression
If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?
Which of the following statements is/are correct in respect of regression coefficients?
1. It measures the degree of linear relationship between two variables
2. It gives the value by which one variable changes for a unit change in the other variable.
Select the correct answer using the code given below.If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?
A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?
If two regression lines between height (x) and weight (y) are 4y – 15x + 410 = 0 and 30x – 2y – 825 = 0, then what will be the correlation coefficient between height and weight?
