Warm-upwith 3.3 Notes on Correlation

The fat and calorie contents of 5oz of 3 kinds of pizza arerepresented by the data points (9, 305), (11, 309) and (13, 316).a. Plot the points. (your graph may have a break along the y-axis)b. Draw a line of best fit by hand and come up with the

equation. (y = mx + b)c. Determine the meaning of the slope and y-intercept in this

situation.d. Make a prediction as how many calories would you think a 15

gram 5oz piece of pizza would have, using your formula from b.

e. Enter the data in L1 and L2 and use the LineReg (ax+b) function to come up with the LSRL for the data.

Answers to Warm-up(9, 305), (11, 309) and (13, 316)

Answers to A.P. Statistics H.W. 3.2 P#3 and 5, E # 9 and 11

P3. As the school year progresses the student’s eraser weighs less (gets smaller). The eraser originally was 91.5 g (y-intercept) and it decreases at a rate of about 1 gram/80 days (slope).

P5. a) The explanatory variable is the student/faculty ration. Theresponse variable is the % of alumni giving.b. Two points on the line are (10, 35) and (15, 25). These are not datapoints but points on the line itself. If I used these to find slope it

result in

c. The y-intercept has no use because there would not be a situation where the student to faculty ratio would be zero.

ratiofacultytostudent5

rategiving%10

A.P. Statistics Answers continued E #9 and 11

E 9. a. I. – E, II. – C, III – A, IV – D, V – B

b. I – A, II – E, III – B, IV – D, V - C

E 11. a. The slope is about 2.5 inches a yearb. The height of boys tend to be 2.5 inches/ year

from ages 2 to 14.c. Depending on the point plugged in, if age 3

was plugged in the resulting equation would be height = 2.5(years) + 31.5

D. A y-intercept of 31.5 would mean that the median height of a newborn is 31.5 inches.

Answers to 3.1 HomeworkStatistics E #1,3 and 5

Statistics 3.1 H.W. Answers continued…

E3. a. II b. IV c. III d. I

E5. a. i. Plots A, B, and C appear the most linear.

ii. Plots A, B, and C appear to have one cluster, Plot D hasabout two.

iii. Plots A and C appear to have possible outliers.

b. Plots and A and C have positive trend. Plot B displays anegative trend.

Remaining Statistics 3.1 h.w. Answers

c. Plot A appears to show the strongest relationship.Plot C shows a possible strong relationship as well.d. I believe if they chose different universities the mayshow slightly weaker correlations.e. For Plot A, the schools with better graduation rates,would more likely product alumni that will donatelater. Plot C, if SAT I scores are higher, these studentsare more likely better prepared to complete collegerequirements for graduation.

Student of the day!Block 4

Student of the day!Block 5

Student of the day!Block 6

Statistics – Looking at the residual plot.Add this to your 3.2 notes on Getting a line.

=_____ _____

baxy ˆ

End of 3.2 Beginning of 3.3 on Correlation

Least Squares Regression Line (LSRL), also least squares lineor regression line where the SSE is as small as possible.

The properties of LSRL: 1)The sum and mean of residuals = 0.

2) The line contains the point averages . ***pg 125 has the rest

3) Most importantly the slope is:

The equation is:

),( yx

21)(

))((

xx

yyxxb

xbby o 1ˆ

x

y

s

srb1

Slope from the correlation coefficientand standard deviation.

Calculating the LSRL step-by-step

A high school counselor wants to see if there is acorrelation between GPA and SAT score. Here are some ofthe data the guidance counselor is looking at.

Sum: _____ _____ _____ ______ _______ _______Mean: ____ _____ _____ _____ to find the bo substitute ( )

xbby o 1ˆ

yx,

3.3 CorrelationCorrelation tells you the strength of the trend.

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.

1

1i i

x y

x x y yrn s s

1( )( )

1 x yr z zn

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 LinReg(ax+b) EnterLineReg(ax +b) L1, L2, Y1 Enter

Notice you get both r and r2!Any theories about the r in this problem? Look at the graph.

A.P. Statistics H.W. Assignment

• Copy formulas and definitions for 3.3 in your vocabulary/formula section of your notebook

• Review your notes and calculator steps for 3.1 to 3.3 Quiz next class.

• Opportunity for a 10 point bonus on the Activitywe are completing October 21st. Bring a bag ofsmall wrapped candy. (round or square) You will geta 10 pt bonus on the activity if you bring a bag.Bring it next class! NO CHOCOLATE!

Statistics H.W.

• 3.2 P # 3 and 5, E#9 and 11.• Copy formulas and definitions for 3.3.• Print out calculator notes soon!• You will need them for the quiz on 3.1 to 3.3

October 21st Friday!