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 the regression coefficient of x on y and y on x are \(- \frac{1}{2}\) and \(- \frac{1}{8}\) respectively, then what is the correlation coefficient between x and y?
For 10 observations on price (x) and supply (y), the following data was obtained:
∑x = 130, ∑y = 220, ∑ x 2= 2288, ∑y 2= 5506 and ∑ xy = 3467.
What is the line of regression of y on x?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?
If X 1, X 2, … X nis a simple random sample without replacement of size n from a finite population of N units with mean μ and variance σ 2, the covariance of (X i, Xj ) will be:
If x = X- \(\bar{X}\) and y = Y - \(\bar{Y}\) and the number of pairs (X, Y) is n, then the Karl Pearson's coefficient of correlation is:
