Question

Find a study that uses linear regression and a line of best fit. What is the Correlation Coefficient? What conclusions can you make about the data? Is there a correlation and how strong is it?

Answer 1

Find a study that uses linear regression and a line of best fit.

The aim of regression is to find the linear relationship between two variables. This is in turn translated into a mathematical problem of finding the equation of the line that is closest to all points observed.

Consider the scatter plot on the below. One possible line of best fit has been drawn on the diagram. Some of the points lie above the line and some lie below it.

When drawing in a regression line, the aim is to make the line fit the points as closely as possible.

Example:

A patient is given a drip feed containing a particular chemical and its concentration in his blood is measured, in suitable units, at one hour intervals. The doctors believe that a linear relationship will exist between the variables.

Time, x (hours)	0	1	2	3	4	5	6
Concentration, y	2.4	4.3	5.0	6.9	9.1	11.4	13.5

We can plot these data on a scatter graph – time would be plotted on the horizontal axis (as it is the independent variable). Time is here referred to as a controlled variable, Concentration is the dependent variable as the concentration in the blood is likely to vary according to time.

What is the Correlation Coefficient? What conclusions can you make about the data? Is there a correlation and how strong is it?

A correlation between variables indicates that as one variable changes in value, the other variable tends to change in a specific direction.

The correlation coefficient is bound between -1 and 1 and tells you the linear relationship between these two variables. A coefficient close to 1 means a strong and positive association between the two variables (when one of them grows, the other does, also, and when one of them decreases, the other one does the same).

A coefficient close to -1 means strong negative association between the two variables, this is, observations with a large value in one of the variables tend to have a small value in the other variable or vice-versa.

A coefficient close to 0 means no linear relation between the two variables.

Hope this will be helpful. Thanks and God Bless You:I