Transcript Warm-up with 3.3 Notes on Correlation

Warm-up
with 3.3 Notes on Correlation
Universities use SAT scores in the admissions process because they
believe these scores provide some insight into how a high school
student will perform at the college level. Suppose the entering
freshmen at a certain college have mean combined SAT scores of 1222
with a standard deviation of 83. In the first semester these students
attained a mean GPA of 2.66 with a standard deviation of 0.56. A
scatterplot showed the association to be reasonably linear, and the
correlation between SAT score and GPA was 0.47.
yˆ  b0  b1 x
a) Identify the following: x, y, sx , and s y
b) If r is the correlation calculate the slope b1.
c) Plug in x, y and b1 to solve for b0 (y-intercept).
d) Write the equation of the regression line.
b0  y  b1 x
b1  r
sy
sx
Student of the day!
Block 1
Student of the day!
Block 2
H.W. Discussion 3.2 P#3 and 4; E#9 and 10
ˆ  bo  b1 x
Calculating the LSRL step-by-step y
A high school counselor wants to see if there is a
correlation between GPA and SAT score. Here are some of
the data the guidance counselor is looking at.
Sum: _____ _____ _____
Mean: ____ _____ _____
______
_______
_______
_____ to find the bo substitute ( x, y )
Use the calculator to find the LSRL
STAT = > CALC Select #8 LinReg(a + bx)
To get correlation go to 2nd 0 for Catalog hit x-1for D.
Find DiagonsticOn highlight it and hit ENTER two
times.
3.3 Correlation
Correlation tells you the strength of the trend.
 xi  x   yi  y 
1
r


 

n  1  sx   s y 
1
r
( z x )( z y )

n 1
OR
r2 is the coefficient of determination. It is the proportion of
variation of the response variable that can be explained
by the explanatory variable.
How to see the residual plot on the calculator!
If the regression line is a good model, we would expect to
find the residuals more or less randomly scattered about
the average residual which is represented by the
horizontal line. No pattern on the residual plot means the
data could be represented by a linear model.
Finding Correlation Coefficient on the Calculator
• In order to find r (correlation coefficient) on your calculator.
• We need to change it from the factory setting by going to
CATALOG (Hit 2nd the 0  zero).
• When in CATALOG your keys are automatically in Alpha so hit
x-1 (where the Green D is located)
• Scroll down to DiagnosticOn and press Enter twice!
Practice: Speed:
20
30
40
50
60
MPG:
24
28
30
28
24
STAT -> Calc Scroll down to 8: LinReg(a+bx) Enter
LineReg(a +bx) L1, L2, Y1 Enter
Notice you get both r and r2!
Any theories about the r in this problem? Look at the graph.
Let’s look at the residual plot
Investigation of
Scatter plots and Residuals
Any observations on
the two Data Sets?
Remember to use
Zoom #9 Zoom Stat
Each time.
Homework
3.3 Pg 141 P#15 and
16, E#27 and 28
Ch. 1 Test
• Double-checked, 12# on FORM A, if you
answered C, you got it right. My answer key
was wrong.
• Bring me your test if your original answer was
A on #12 if you had FORM A.
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•
•
•
•
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Monday is 3.1 to 3.3 Quiz
Know all vocabulary and formulas from 3.1 to 3.3
Know how create a scatter plot and find the Line of best fit.
Know how to calculate the LSRL, how to extrapolate and
calculate the residual for a particular piece of data.
Be able to interpret the slope and y-intercept in the context
of the problem
Know how to describe scatter plots: Shape, Trend Strength
and under Shape: Linearity, Clusters and outlier.
Know how to calculate the SSE
Answers to A.P. Statistics H.W. 3.2 P#3 and 4, E # 9 and 11
P4. a. The slope is about 0.8 b. This means as hand length increases
by 1 cm, the width would increase by 0.8 cm.
c. handwidth 1.7  0.8 handlength
d. A possible explanation is that the points represent those
students that measured hand width by not spreading fingers apart.
If the cluster of points below was removed then the slope becomes
steeper.
P5.
E #9
E #10