Question

What determines how well a regression equation will predict values of the y-variable from known values of the x-variable? (A) What values or points make-up the regression line? (B) What two points are always found on the regression line? (Hint: These two points can be used to quickly draw the regression line) Explain why the regression line the “best fitting” line that can be plotted through the points in a scatter diagram? Describe how predicted y-values plotted near the point of averages differ in their accuracy compared to predicted y-values plotted further away from the point of averages.

Answer 1

Adjusted & are the measures which determines how well a regression equation will predict values of the y-variable from known values of the x-variable.

All the points of independent variables to dependent variable make the best possible regression line.

& are the two points are always found on the regression line.

Line that fits the data "best". One for each data point. One way to achieve this goal by "least squares criterion," That means "minimize the sum of the squared prediction errors." Following steps are the procedure to LR:

• The equation of the best fitting line is:  
• The values and that make the sum of the squared prediction errors the smallest it can be.
• We need to find the values and   that minimize: