What would you look like if your name was Tai Shan?

Parents names:Mother: Mei Xiang

Father: Tian Tian

Background:

August 8 at 2.6 pounds

born on July 9, 2005On August 2, learned gender male – 1.82 lbsNamed on day 100 – Tai Shan means “peaceful mountain”

Dec. 2009 he moved to China

Just over 1 month old

October 12 – 96 days old

The Data

Age in days weight (lbs)62 21.2573 22.584 24.796 25.5

105 27.1115 28.5125 28.6136 31.2158 36.6187 37249 44.4

Categorical orQuantitative?

How many variables?

So what kind of graph is

appropriate?

data source: http://nationalzoo.si.edu/Animals/GiantPandas/PandaFacts/cubgrowth.cfm

Cut data just after this picture was taken. Tai began eating bamboo rather than just nursing….so the growth rate changed.

http://www.flickr.com/photos/56581511@N00/7192756932/

Graphed using excel spreadsheet

50 100 150 200 250 3000

5

10

15

20

25

30

35

40

45

50

Age in days

Wei

ght i

n po

unds

So what should a student write about this graph?

Graphed using excel spreadsheet

50 100 150 200 250 3000

5

10

15

20

25

30

35

40

45

50

Age in days

Wei

ght i

n po

unds

Form – Outliers – Direction – Strength – IN CONTEXT!!!

There appears to be a strong, positive, linear relationship between age and weight. Day 249 at weight 44.4 might be a possible outlier.

To get the equation of theBEST fit line using a calculator.

First enter the data into List1

and List2.

PushSTATEDIT

To get to the lists.

If a list already has data you need to delete, use the arrow to

buttons to highlight the LIST NAME at the top.

Then pushCLEARENTER

Now enter the data.

Handy side note: 2nd – QUIT

Will always get you “home”.

Push 2nd then y=To get to the statplots

Set up your graph.

Note: L1 and L2 are found above the numbers 1 and 2. Push 2nd and then the number to enter a list name.

Go home! Well, push 2nd – quit

From here, you may push graph

but you probably won’t see it.

We need a proper window.

PushZOOM 9

Ta Da!

Now to get the equation of the linear regression line(Or Least-squares regression line, if you want)

Push STAT CALC

8 Linreg

Old program:

LinReg(a+bx)L1,L2,Y1

So what’s all this?

If you didn’t get r and r2 and you want them, push 2nd, 0, and go down to diagnostics ON and hit enter twice. Then try again.

The equation:ŷ = 13.7403 + .1268 x

LinReg y = a + bx a = 13.74034878 b = .126767024 r2 = .9783259151 r = .9891035917

What does the slope mean? What would you write?

ŷ = 13.7403 + .1268 x

First, make it a fraction. 1

For every 1 day increase in age, the weight increases .1268 pounds, on average.

y-intercept?

If the baby panda was 0 days old, he would weight about 13.7403 pounds.

Well, that’s a silly extrapolation!

ŷ = 13.7403 + .1268 x

FYI : r is called the correlation coefficient and is ALWAYS between -1 and 1. The closer it is to -1 or 1 the more the points line up. So r = .9891 suggests a very strong, positive, linear relationship between age and weight.

r2 is called the coefficient of determination and tells us the amount variation the two variables have in common.r2 = .978 means that 97.8% of the variation in weight is explained by the variation in age.

LinReg y = a + bx a = 13.74034878 b = .126767024 r2 = .9783259151 r = .9891035917

So why is all this a big deal?

Now we can use our equation to make predictions.

ŷ = 13.7403 + .1268 x

How much would you predict Tai Shan weighed at 348 days?

ŷ = 13.7403 + .1268 (348)ŷ = 57.9 pounds

y = 54 pounds

How much would you predict Tai Shan weighed at 3 years?

ŷ = 152 pounds

y ≈ 200 pounds

ŷ = 13.7403 + .1268 x ŷ = 13.7403 + .1268 (1095)

To determine if a linear model is really appropriate, we should check the residual plot.

Go back into your statplot: 2nd , y= , 1

To put resid into the ylist,2nd

statresid

Note: resid will only come up IF you have just

previously done the linear regression.

age in days

residual

62 249

2.83

- 0.9

Residual Plot

The residual plot shows no obvious pattern so a linear model is a good choice.

Tia Shan just celebrated his 7th birthday at his new home in China.