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

What would you look like if your name was Tai Shan? Parents names: Mother: Mei Xiang Father: TianTian

Background: born on July 9, 2005 On August 2, learned gender male – 1.82 lbs Named on day 100 – Tai Shan means “peaceful mountain” Dec. 2009 he moved to China August 8 at 2.6 pounds

Just over 1 month old

October 12 – 96 days old

The Data Categorical or Quantitative? So what kind of graph is appropriate? How many variables? 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.

Graphed using excel spreadsheet So what should a student write about this graph?

Graphed using excel spreadsheet 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. Push STAT EDIT To get to the lists. First enter the data into List1 and List2.

If a list already has data you need to delete, use the arrow to buttons to highlight the LIST NAME at the top. Then push CLEAR ENTER 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. Push ZOOM 9

Ta Da!

Now to get the equation of the linear regression line (Or Least-squares regression line, if you want) Old program: LinReg(a+bx)L1,L2,Y1 Push STAT CALC 8Linreg

So what’s all this? LinReg y = a + bx a = 13.74034878 b = .126767024 r2 = .9783259151 r = .9891035917 The equation: ŷ= 13.7403 + .1268 x 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.

ŷ = 13.7403 + .1268 x What does the slope mean? What would you write?

ŷ = 13.7403 + .1268 x 1 First, make it a fraction. 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!

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

So why is all this a big deal?

Now we can use our equation to make predictions. How much would you predict Tai Shan weighed at 348 days? ŷ = 13.7403 + .1268 x ŷ = 13.7403 + .1268 (348) ŷ = 57.9 pounds y = 54 pounds

How much would you predict Tai Shan weighed at 3 years? ŷ = 13.7403 + .1268 x ŷ = 13.7403 + .1268 (1095) ŷ = 152 pounds y ≈ 200 pounds

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 stat resid Note: resid will only come up IF you have just previously done the linear regression.

Residual Plot 2.83 r e s i d u a l - 0.9 62 249 age in days The residual plot shows no obvious pattern so a linear model is a good choice.

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

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