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 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 ?
Two variates, x and y, are uncorrelated and have standard deviations σ xand σ yrespectively. What is the correlation coefficient between x + y and x – y?
If the covariance between x and y is 30, variance of x is 25 and variance of y is 144, then what is the correlation coefficient?
If, in a series. there are m items whose ranks are common, then which factor is added for correction for each repeating value in both the series?
