0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Best Fit Line

377

Published on

Fitting data to a line and finding the slope

Fitting data to a line and finding the slope

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total Views
377
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
8
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1.
• When points lie nearly on a line, it is useful to determine an equation for a line that lies on or comes close to the points.
• 2. Usually, there is no single line that passes through all the data points, so you try to find the line that best fits the data. This is called the best-fitting line . best-fitting line . There are several ways to find the best-fitting line for a given set of data points. In this lesson, you will use a graphical approach. – 8 8 6 4 2 – 2 – 4 – 6 0 2 4 6 – 2 – 4 – 6 – 8 F ITTING A L INE TO D ATA
• 3. Write an equation of your line. The winning Olympic discus throws from 1908 to 1996 are plotted in the graph. Approximate the best-fitting line for these throws. Approximating a Best-Fitting Line D ISCUS T HROWS Years since 1900 Distance (ft) 0 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250
• 4. S OLUTION Find two points that lie on the best-fitting line , such as ( 8, 138 ) and ( 96, 230 ) . Find the slope of the line through these points. Approximating a Best-Fitting Line Years since 1900 Distance (ft) 0 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 ( 96, 230 ) . (96, 230) ( 8, 138 ) ( 8, 138 )
• 5. y = m x + b 129.6 = b Write slope intercept form. Substitute 1.05 for m , 8 for x , 138 for y . Simplify. Solve for b . 138 = ( 1.05 ) ( 8 ) + b y = m x + b 138 = 8.4 + b 92 88 = 1.05 Years since 1900 Distance (ft) 0 8 16 24 32 40 48 56 64 72 80 88 96 104 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 (96, 230) ( 8, 138 ) 230 – 138 96 – 8 = An equation of the best-fitting line is y = 1.05 x + 129.6. y 2 – y 1 x 2 – x 1 m = In most years, the winner of the discus throw was able to throw the discus farther than the previous winner. Approximating a Best-Fitting Line 230 – 138 96 – 8 = 92 88 = 1.05
• 6. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have a positive correlation , which means that the points can be approximated by a line with a positive slope .
• 7. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have a negative correlation , which means that the points can be approximated by a line with a negative slope .
• 8. D ETERMINING THE C ORRELATION OF X AND Y In this scatter plot, x and y have relatively no correlation , which means that the points cannot be approximated by a line.
• 9. D ETERMINING THE C ORRELATION OF X AND Y Positive Correlation No Correlation Negative Correlation T YPES OF C ORRELATION