Download Unit 2 – Two Variable Stats Summary for the Test

Unit 2 – Two Variable Stats Summary for the Test
Summary of Concepts to know for the unit test:
1. Correlations (Positive, Negative, Strong, Weak, None)
2. Correlation Coefficient (r is a value between –1 and 1; it suggests whether the correlation for linear
fits has a positive or negative slope and something about the strength of the correlation)
3. Coefficient of Determination (R2 is a value between 0 and 1; when the value is closer to 1, the points
are closer to the lobf/cobf; it is used for all models linear, quad, cubic, etc…)
4. Median-Median Line (it is created using three medians; it is not the line of best fit but rather a line of
good fit)
5. Residuals and Residual Plots (When a good choice of model is used to fit through some data, the
residuals in the residual plot should show no apparent pattern and be distributed nearly equally above
and below the x-axis. If the residuals are all of the same sign then the attempted lobf/cobf is not
correct and should be shifted up/down).
6. Know how to write the coordinates of the residuals from a graph or from information about the fit and
data points.
7. Correlation does not always create causation (Know the meaning of cause and effect relationships,
reverse cause and effect relationships, common cause relationships and accidental relationships).
8. Know how to use the TI-83 to create regressions(linear, quadratic, cubic, etc)
9. Know how to use the TI-83 to make predictions using a modeled fit.
10. Know how to use the TI-83 to calculate the residuals.
11. Know how to deal with calc errors; dim mismatch, window errors, etc..
TI-83 Key Functions
** Remember to turn diagnostics back on whenever you reset a TI-83 **
1. To reset: prg. starter, enter.
2. To turn diagnostics on: 2nd, 0, x-1, DiagnosticsOn, enter, enter.
3. To enter data set: Stat, Enter
4. To Set up the window: Window
5. To plot your data points:: 2nd, y=, select “on”, graph
6. To create a linear regression: stat, >, 4 (LinReg(ax+b)), then enter L1, L2, Y1 to put the linear
equation into the Y1 location. Press enter when you screen says, “LinReg(ax+b) L1, L2, Y1”. Y1 can
be written by pressing vars, >, enter, enter.
7. To create other regressions follow the same as instruction 5 but change “LinReg” to another option.
You can also pull the x and y data sets from another list line other than L1 and L2 and enter the
regression equation to another location other than Y1 if you don’t want to erase what is already in Y1.
8. To get the residuals, enter your data(x,y) into L1 and L2. put your cursor on top of L3 and press 2nd,
stat, RESID, enter. The calculator can not determine the residuals until a lobf/cobf has been created.
9. To make a prediction/extrapolate using your regression model, with the graph on the screen press 2nd,
trace and enter a value for “x =”. Note: you may have to use the up/down arrow to make sure that you
are using the correct model.
More Practice: pg 68-70 # 5abc, 6, 7, pg 71-72 # 3 (graph lobf), 4, 6, 9
pg 68 - 70 # 4, 9, pg 72 # 7, 8, 10
Activity
Create a linear and quadratic regression on your TI-83 for the
following data set:
Year of
birth Life Expectancy
1921
60
1931
61
1941
64
1951
68.5
1961
70
1971
72.5
1981
75.5
1991
78
2001
79.5
a) Record the coefficient of determination for each model.
b) Which model fits the data better?
c) Which model seems more reasonable scientifically? Explain.
d) Is there ever a situation where a linear model will fit the data better than a
quadratic model?
e) For the line of best fit, count the number of residuals that are positive.
Does this amount seem reasonable?
f) What will be the life expectancy for a baby born in 2011? 2100?