Name:  ______________________________                        Date:  __________________

Linear Regression Lab

You will be using the website:

http://www.illuminations.nctm.org/imath/912/LinearRelationships/student/index.html#first

This website allows the students to plot points and it will do the linear regression.

Given the following points determine the linear regression by hand:

To complete the linear regression you need to estimate the equation on the line in slope-intercept form: y = mx + b.

You need to estimate your “m” and your “b” given some coordinates.

1.  Find the linear regression given:

(0, 2)  (3, 0)  (1, 1.5)  (-2, 3)

Plot the four points on a graph.  Draw a line through the 4 points as close to the center of the points while hitting 2 coordinates.

Pick the 2 points you intersected and determine the slope (m) using the formula:

                                                                                       m = ___________

 

 

To find your y-intercept (b) use the slope-intercept form; y = mx + b.

You have found a slope, now pick a coordinate from above and fill in the y, m, and x and solve for b.  You could also estimate your y-intercept by the line you drew on your hand written graph.

                                                                                                            b = ___________

 

Now that you have the “m” and “b”, write the equation of the line:  y = ___________

2.  Go the above website.

Note:  It may be difficult to plot the points on the website, just get as close as possible.

Note:  Your linear regression will probably not be exactly like the website.  That is okay.  The intention is that they are close.

Plot the point and see how close your equation is to the one on the website.

How close are the linear regressions? 

 

Observations:

 

 

 

 

Try these other examples:

(-2, -2)  (0,0)  (1, 1)  (2, 1)

                           

(-3, -1)  (-1, 1)  (0.5, 2)  (3, 4)

 

 

 

 

 

 

One Solution to lab:

Name:  ______________________________                        Date:  __________________

Linear Regression Lab

You will be using the website:

http://www.illuminations.nctm.org/imath/912/LinearRelationships/student/index.html#first

This website allows the students to plot points and it will do the linear regression.

Given the following points determine the linear regression by hand:

To complete the linear regression you need to estimate the equation on the line in slope-intercept form: y = mx + b.

You need to estimate your “m” and your “b” given some coordinates.

1.  Find the linear regression given:

(0, 2)  (3, 0)  (1, 1.5)  (-2, 3)

Plot the four points on a graph.  Draw a line through the 4 points as close to the center of the points while hitting 2 coordinates.

 

Pick the 2 points you intersected and determine the slope (m) using the formula:

                                                                                       m = Varies

 

 

To find your y-intercept (b) use the slope-intercept form; y = mx + b.

You have found a slope, now pick a coordinate from above and fill in the y, m, and x and solve for b.  You could also estimate your y-intercept by the line you drew on your hand written graph.

                                                                                                            b = Varies

 

Now that you have the “m” and “b”, write the equation of the line:  y = -0.59x + 1.9

2.  Go the above website.

Note:  It may be difficult to plot the points on the website, just get as close as possible.

Note:  Your linear regression will probably not be exactly like the website.  That is okay.  The intention is that they are close.

Plot the point and see how close your equation is to the one on the website.

How close are the linear regressions? 

Website:  y = -0.58x +1.89

Answer:  y = -0.59x + 1.92

Observations:

Not the same, but similar.

 

 

Try these other examples:

(-2, -2)  (0,0)  (1, 1)  (2, 1)

 

  

(-3, -1)  (-1, 1)  (0.5, 2)  (3, 4)