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, 2005 On August 2, learned gender male – 1.82 lbs Named on day 100 – Tai Shan means “peaceful mountain” Dec he moved to China

Just over 1 month old

October 12 – 96 days old

The Data Age in daysweight (lbs) Categorical or Quantitative? How many variables? So what kind of graph is appropriate? data source:

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. First enter the data into List1 and List2. Push STAT EDIT 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 push CLEAR ENTER Now enter the data. Handy side note: 2 nd – QUIT Will always get you “home”.

Push 2 nd then y= To get to the statplots Set up your graph. Note: L1 and L2 are found above the numbers 1 and 2. Push 2 nd and then the number to enter a list name.

Go home! Well, push 2 nd – 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) Push STAT CALC 8 Linreg Old program: LinReg(a+bx)L 1,L 2,Y 1

So what’s all this? If you didn’t get r and r 2 and you want them, push 2 nd, 0, and go down to diagnostics ON and hit enter twice. Then try again. The equation: ŷ = x LinReg y = a + bx a = b = r 2 = r =

What does the slope mean? What would you write? ŷ = 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 pounds. Well, that’s a silly extrapolation! ŷ = 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. r 2 is called the coefficient of determination and tells us the amount variation the two variables have in common. r 2 =.978 means that 97.8% of the variation in weight is explained by the variation in age. LinReg y = a + bx a = b = r 2 = r =

So why is all this a big deal?

Now we can use our equation to make predictions. ŷ = x How much would you predict Tai Shan weighed at 348 days? ŷ = (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 = x ŷ = (1095)

To determine if a linear model is really appropriate, we should check the residual plot. Go back into your statplot: 2 nd, y=, 1 To put resid into the ylist, 2 nd stat resid Note: resid will only come up IF you have just previously done the linear regression.

age in days residualresidual Residual Plot The residual plot shows no obvious pattern so a linear model is a good choice.

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