Doffy said:Two normal equations are given :
5a + 10b = 40
10a + 25b = 95
What is the regression line of y on x?
I can easily find the common points from both the equations but how do I find the regression coefficeint?
A line of regression, also known as a regression line, is a straight line that best represents the relationship between two variables in a dataset. It is used to predict the value of one variable based on the value of another variable.
The line of regression is calculated using a statistical method called linear regression. This involves finding the best-fitting line that minimizes the distance between the line and all the data points in a dataset. The slope and intercept of the line are determined using a formula that takes into account the mean of the two variables and the covariance between them.
The slope of the line of regression represents the rate of change between the two variables. In other words, it indicates how much the dependent variable (y) changes for every unit increase in the independent variable (x). A positive slope indicates a positive relationship, while a negative slope indicates a negative relationship.
The intercept of the line of regression represents the value of the dependent variable (y) when the independent variable (x) is equal to 0. It is not always meaningful to interpret the intercept, as it depends on the context and the variables being studied. In some cases, the intercept may not have a practical interpretation.
Yes, the line of regression can be used for prediction by plugging in a value for the independent variable (x) and solving for the corresponding value of the dependent variable (y). However, it is important to note that the line of regression is only accurate for predicting values within the range of the data used to calculate it. Extrapolating beyond this range may not yield accurate predictions.