###### Asked in StatisticsMath and Arithmetic

Statistics

Math and Arithmetic

# Why is it important to know the regression line?

## Answer

###### Wiki User

###### July 14, 2009 1:49PM

Yes, that is what allows you to predict data values based on the information you have. It also tells you other things about the data set such as the correlation.

## Related Questions

###### Asked in Math and Arithmetic, Statistics

### Why are there two regression lines?

There are two regression lines if there are two variables - one
line for the regression of the first variable on the second and
another line for the regression of the second variable on the
first. If there are n variables you can have n*(n-1) regression
lines.
With the least squares method, the first of two line focuses on
the vertical distance between the points and the regression line
whereas the second focuses on the horizontal distances.

###### Asked in Math and Arithmetic, Statistics

### What is regression line?

Regression techniques are used to find the best relationship
between two or more variables. Here, best is defined according to
some statistical criteria.
The regression line is the straight line or curve based on this
relationship.
The relationship need not be a straight line - it could be a
curve. For example, the regression between many common variables in
physics will follow the "inverse square law".

###### Asked in Math and Arithmetic

### What characteristic makes regression line of best fit?

The equation of the regression line is calculated so as to
minimise the sum of the squares of the vertical distances between
the observations and the line.
The regression line represents the relationship between the
variables if (and only if) that relationship is linear. The
equation of this line ensures that the overall discrepancy between
the actual observations and the predictions from the regression are
minimised and, in that respect, the line is the best that can be
fitted to the data set. Other criteria for measuring the overall
discrepancy will result in different lines of best fit.

###### Asked in Statistics, Algebra

### What is the relationship between correlation coefficient and linear regreassion?

A correlation coefficient is a value between -1 and 1 that shows
how close of a good fit the regression line is. For example a
regular line has a correlation coefficient of 1. A regression is a
best fit and therefore has a correlation coefficient close to one.
the closer to one the more accurate the line is to a non regression
line.

###### Asked in Statistics

### Can anyone tell what is important in regression analysis?

The question is vague. Regression can be a complex analysis, and
which information is important depends greatly on what you are
using the results for.
But very generally, if you are using regression as a hypothesis
test, then the F (test statistic), r-square (effect size), and p
(significance level), will be important. If you are using
regression for predicting a value of Y based on X, then the slope
of the regression line (b) and its intercept with the Y axis (a)
are needed for the regression equation: Y = a + bX.
Computer programs such as SPSS also test the statistical
significance of both the intercept and the slope by comparing them
to zero, and they will report several other numbers related to
these tests. However, this may or may not be information that the
researcher is interested in. Again, it all depends on the
situation.

###### Asked in Math and Arithmetic

### If the regression sum of squares is large relative to the error sum of squares is the regression equation useful for making predictions?

If the regression sum of squares is the explained sum of
squares. That is, the sum of squares generated by the regression
line. Then you would want the regression sum of squares to be as
big as possible since, then the regression line would explain the
dispersion of the data well.
Alternatively, use the R^2 ratio, which is the ratio of the
explained sum of squares to the total sum of squares. (which ranges
from 0 to 1) and hence a large number (0.9) would be preferred to
(0.2).

###### Asked in Statistics

### What is Definition of linear regression and correlation in statistics?

Whenever you are given a series of data points, you make a
linear regression by estimating a line that comes as close to
running through the points as possible. To maximize the accuracy of
this line, it is constructed as a Least Square Regression Line
(LSRL for short). The regression is the difference between the
actual y value of a data point and the y value predicted by your
line, and the LSRL minimizes the sum of all the squares of your
regression on the line.
A Correlation is a number between -1 and 1 that indicates how
well a straight line represents a series of points. A value greater
than one means it shows a positive slope; a value less than one, a
negative slope. The farther away the correlation is from 0, the
less accurately a straight line describes the data.

###### Asked in Math and Arithmetic, Statistics

### What is alpha in regression analysis?

Alpha is not generally used in regression analysis. Alpha in
statistics is the significance level. If you use a TI 83/84
calculator, an "a" will be used for constants, but do not confuse a
for alpha. Some may, in derivation formulas for regression, use
alpha as a variable so that is the only item I can think of where
alpha could be used in regression analysis.
Added:
Though not generally relevant when using regression for
prediction, the significance level is important when using
regression for hypothesis testing.
Also, alpha is frequently and incorrectly confused with the
constant "a" in the regression equation Y = a + bX where a is the
intercept of the regression line and the Y axis. By convention,
Greek letters in statistics are sometimes used when referring to a
population rather than a sample. But unless you are explicitly
referring to a population prediction, and your field of study
follows this convention, "alpha" is not the correct term here.