In the equation for linear regression $Y=a+bX$, $b$ stands for:​

Correct option is B

Sol.
In the linear regression equation $Y=a+bX$:

• $a$ is the intercept, representing the value of $Y$ when $X=0$.
• $b$ is the regression coefficient, also known as the slope of the line. It measures the change in the dependent variable $Y$ for a one-unit change in the independent variable $X$.
• $b$ indicates the strength and direction of the relationship between $X$ and $Y$. If $b$ is positive, the relationship is direct; if negative, it is inverse.

The regression coefficient $b$ is calculated as:
$b=$

It shows how $X$ influences $Y$, playing a central role in predictive analytics.

Information Booster:

1. The regression line minimizes the sum of squared errors (least squares method).
2. The slope $b$ provides insight into the magnitude and direction of influence.
3. Regression assumptions include linearity, independence, homoscedasticity, and normal distribution of residuals.
4. Applications include trend prediction, forecasting, and finding relationships in data.

Additional Information:

• Option 1 (Y intercept on X): Incorrect; the intercept $a$ refers to $Y$, not $X$.
• Option 2 (Regression coefficient): Correct; $b$ measures the effect of $X$ on $Y$.
• Option 3 (X intercept on Y): Incorrect; the X-intercept is not directly part of the regression equation.
• Option 4 (Constant): Incorrect; $a$ is the constant, not $b$.