BELLWORK

1. Max is a computer salesman. For each day that he works, he receives $50 plus a fixed commission amount per computer. Max is currently earning $122 for the sales of 6 computers. If he sells an additional 5 computers, what will be his new daily earning?

2. Write the equation in the standard (x,y) coordinate plane that is perpendicular to the line 4x-3y=9 and containing the point (8, 2).

ALGEBRA 2Lesson 1.5

Scatter Plots and Least Squares Lines

OBJECTIVES:

• Create a scatter plot and draw an informal inference about any correlation between the variables.

• Use a graphics calculator to find an equation for the least-squares line and use it to make predictions of estimates.

Why: Scatter plots and least-squares lines can be used to analyze trends in society.

A scatter plot below uses the above data with the calculus midterm score on the Y-axis and SAT score on the X-axis.

Scatter Plot of the Test scores

We can see that the scatter plots can be useful to find any relationship that may exist among the data. Also, the scatter plots are helpful in analyzing the data and the errors in the linear regression analysis can be found easily.

Notes: There are 3 types of scatter plots that show different trends.

1.) Positive Correlation

2.) Negative Correlation

3.) Zero Correlation

PROFESSOR EDWARD BURGER

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TO PREPARE YOUR CALCULATOR:

2nd

To set up the calculator to do statistics operations…

- Scroll down and turn

To set up the coordinate plane “window

- Set the dimensions for the x-axis and y-axis

**Leave the x scale and y scale at 1 **

To set up the calculator to draw a scatter plot:

then hit,

Then choose,

0 Diagnostics ON

window

Y=1: Plot 1 …

On

On L1 L2 ▫

2nd

Data:

Steps on how to CLEAR a list in your calculators:

Steps on how to enter the information in your calculators:

Enter the x-values and y-values. You must hit “ENTER” after

each number. Do not scroll down or you will get an error message.

To see the scatter plot, hit

To calculate the least-squares line (line that fits the data), hit

Choose Then hit

X 2 4 6 8 10

Y 11 6 8 4 7

Stat Enter4 clr List

1, 2nd 2 Enter

Stat 1 edit

Enter graph

StatCALC

4 LinReg (ax +b) Enter Enter

THIS IS WHAT YOU HAVE…y=ax + b

a = -.5 (slope)

b= 10.2 (y-intercept)

r= -.61 (The correlation coefficient indicates how closely the data points cluster around the least squares line.)

y= -.5x + 10.2 (The equation of the least-squares line.)

Data:

Don’t forget to change your window to correspond with the data!

y= ax + b

a = 1.89 (slope)

b= 14.75(y-intercept)

r= 0.99 (The correlation coefficient indicates how closely the data points cluster around the least squares line.)

y= 1.89x + 14.75

x 0 2 3 6 7 9 12

y 14 19 22 26 26 32 38

Data:

Let x = the number of years after 1980

y= ax + b

a = 4.57 (slope)

b= 84.29(y-intercept)

r= 0.99 (The correlation coefficient indicates how closely the data points cluster around the least squares line.)

y= 4.57x + 84.29

Based on the linear regression line, what would you predict the CPI to be in the year 2012?

ANS: 231

X (year

)

1980 1982 1984 1986 1988 1990 1992

Y (CPI)

82 97 104 110 118 131 140

• Create a scatter plot of the data in the table below. • Describe the correlation.• Find an equation for the line of best fit.

x 1 4 3 7 7 4 11

y 32 53 41 33 48 52 66

2.29 34.30y x

.63r

HOMEWORKLesson 1.5

Pgs. 40-41

(9-11,13-20)