Get out your Interpretation WS!
You will be able to predict values based on a regression line.
You will be able to communicate the risk in extrapolation.
You will be able to define and find a residual.
Today’s Objectives:
Warm UpThe table shows the cost of visiting a working ranch for one day and night for different numbers of people.
1. Make a scatterplot in your calculator of the table below.
2. Find the correlation coefficient, . Write the equation.
3. What is the slope of the line? Explain in words what the slope means in the setting.
4. What is the y-intercept? Explain in words what the y-intercept means in the setting.
Number of people (x) 5 7 9 11 13Cost ($) 200 340 410 490 560
Homework Check
.99𝒚=−𝟎 .𝟑+𝟎 .𝟏𝟔𝒙
0.16; when the meal cost increases by $1 then the tip increases by $0.16
$1.35
-0.3; if there is no meal cost there is no tip
Homework Check
.99𝒚=𝟔𝟑 .𝟗𝟑+𝟔 .𝟎𝟗𝒙
6.09; for every hour extra spent studying, then exam grade increases by 6.09%.
100.47%
63.93; if you do not study you will make a 63.93%
Homework Check
.9992 or 1𝒚=−𝟏𝟓𝟔 .𝟏𝟒+𝟒 .𝟑𝟔𝒙
4.36; so if the length of the shark goes up by 1 then the weight goes up by 4.36
170.86
-156.14; no statistical significance
Homework Check
.997 or 1
𝒚=−𝟏𝟗 .𝟖𝟏+.𝟒𝟐𝒙.42; if a man grows one inch taller, then his shoe size will increase by .42 of a size
72.17 inches
-19.81; no statistical significance
ExtrapolationPredicting Y values for X values outside the range of X values observed in the data is extrapolation.
This is risky, because you have no evidence that the linear relationship you have seen in the scatterplot continues to hold in the new X region.
Extrapolated values can be entirely wrong.
Why is Extrapolation Risky?The table shows the heights of the average boy as he ages.1. Make a scatterplot in your calculator of the table below.
2. Find the correlation coefficient, .3. Use your calculator to draw the regression line. Write
out the equation of the regression line. 4. What is the slope of the line? Explain in words what the
slope means in the setting.5. What is the y-intercept? Explain in words what the y-
intercept means in the setting.
# of Years Old 2 3 4 5 6 7 8Height (inches) 31 33 37 40 42 44 45
ExtrapolationUse your equation () to predict the following situations.
1. 10 year-old boy
2. 17 year-old boy
3. 55 year-old man
ConclusionYou can see now that you have no evidence that the linear relationship between the boy’s heights between 2 and 8 years continues to hold in the new X region, 55 years.
What do you expect to happen to the scatterplot? To the regression line?
# of Years Old 2 3 4 5 6 7 8 17 55Height (inches) 31 33 37 40 42 44 45 69 72
ExtrapolationAdd the values to your L1 and L2 lists.
Do not clear your y= !!!!!
STAT 8: L1, L2, Y2 Enter Graph
***The first line was the original regression line, the second was the new regression line which takes 17 and 55 into account.
ExtrapolationThe second line you see graphed is the regression line that CAN be used to predict the height of any man ages 2-55. And still, you cannot predict the height of a 74 year old man because you have no evidence that the linear relationship you have seen in the scatterplot continues to hold in the new X region.
Residuals WorksheetGet out your calculator and a pencil/pen.
Everyone will get a worksheet.
Keep your notebooks open so that you can continue to take notes.
ResidualsOn your worksheet make a scatterplot (by hand) of the following female height data.
Now make a scatterplot on your calculator and draw a regression line. Write the equation on your worksheet.
# of Years Old 6 8 10 11 13 15 17 20Height (in) 41 45 51 52 60 63 64 65
Residual NotesWe will use this information to depict what a residual is.
The definition of a residual is the difference between an observed value of and the value predicted by the regression line.
Observed values are in the given chart. Predicted values come from the calculator.
𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑦−𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 𝑦We need to find the heights predicted by the regression line for all of the ages. These predicted heights will be written at the bottom of your worksheet.
You may do one of two things1. Plug in each age for in the equation OR
2. Use your calculator.Press TRACE arrow downType in new value and ENTERThe type the second and ENTER
Finding the ResidualAt the top of the worksheet use the equation to find each residual…
The height from the table goes first and you subtract the predicted heights.
Plotting Residual PointsDraw a horizontal line at 0. This is your zero line or base line.
On the Residual Plot, you will plot each of the ordered pairs you have found.
Each ordered pair is i.e. for the 6 year old:
Final Residual PlotConnect each plotted point to the zero line with a vertical line.
This plot help you visualize the variation of the predictions vs. the actual data points. The zero line represents the actual data.
Residual NotesPoints underneath the residual’s zero line have a negative residual.So, these points are under-predicted.
Points underneath the residual’s zero line have a positive residual.So, these points are over-predicted.
Residual Plot on the Calculator2ND y=
Select Plot 1
Change the Ylist from L2 to 7:RESID. (To find RESID press 2nd STAT, arrow down to RESID, and press ENTER)
Zoom 9:
Another Residual ProblemUse your calculator to make a scatterplot of the summary of the cost of a catered dinner for different numbers of people.
Draw the regression line. Find the equation.Find each predicted prices.Find each residual.Draw the zero line. Plot all residuals on a residual plot.
# of People, x 12 15 18 20 21 26 32 35Cost ($), y 100 110 125 132 135 141 149 155
Answers Predicted $107.85114.51121.16125.60127.82138.92152.24158.90
Residuals-7.85-4.513.846.47.182.08-3.24-3.9
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
876543210-1-2-3-4-5-6-7-8
Ticket Out The DoorOn a 3x5 card please write your name and answer the following…
3 - things you learned today
2 - questions you still have
1- summarize the lesson in ONE sentence
HOMEWORKResiduals WorksheetDue next Monday
HAPPY THANKSGIVING!
