Today’s Objectives:

Get out your Guess My Age WS!

You will be able to draw a line of regression.

You will be able use the least-squares method for finding the regression line.

Today’s Objectives:

Warm Up1. What is the explanatory variable?

2. What is the response variable?

3. Make a scatterplot using your calculator that displays the relationship.

4. Describe the direction, form, and strength of the relationship.

5. Find the correlation coefficient, r.

6. What do you conclude about when babies learn to crawl?

Vitruvius and the Ideal ManSplit up into groups of 2-3 people.

Turn to pg. 168

We will be working through Activity 4.2 as a class

***#6—only find

Vitruvius and the Ideal Man

AndrewHunterJamalEliDianaHannahCora

BenitaHakeemSerenaJessicaBrandyLathamKatia

Height ArmName (inches) (inches)

Height ArmName (inches) (inches)

Regression Lines Correlation shows the relationship between two quantitative variables.

A regression line is a summary of a straight line relationship between those two variables.

It describes how the response variable changes as the explanatory variable changes.

Body weight vs. Backpack weightTurn to pg. 159

Use your calculator to make a scatterplot of this data.

Describe the direction, form, and strength of the relationship between these variables.

Body Weight vs. Backpack WeightThe figure below is the same scatterplot with a regression line added. This line allows us to summarize the overall pattern.

Body Weight vs. Backpack WeightSuppose that a last minute hiker is assigned to the group. He weighs 150 lbs. Can we predict his backpack weight?

Energy vs. TemperatureThis scatterplot compares average monthly temperature and average amount of gas consumed per day.

ComparisonsWhat does correlation have to do with the accuracy of a prediction?

How Do You Find a Regression Equation?The most common way to find a regression equation is using the least-squares method.

The idea behind this method is that a line makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

Least-Squares Regression

Least-Squares RegressionUsing the formula for finding the least-squares regression is the calculator’s job.

The equation of a line is _______________

In statistics it is written as ______________𝑦=𝑎+𝑏𝑥

Least-Squares Regression

:

:

𝑦=𝑎+𝑏𝑥

Using Least-SquaresTo use the equation for prediction, just substitute your -value into the equation and calculate the resulting -value.

Body Weight vs. Backpack WeightYou should already have the chart on pg. 159 in your calculator. If not go there now and enter that information into your L1 and L2.

Make a scatterplot.

Now we will use our calculators to draw a regression line.

Calculator HintsSTAT arrow right to CALC choose 8:LineReg(a+bx)

(***notice how similar 4: and 8: are)

Type L1 comma L2 comma Y1 (to find Y1 press VARS Y-VARS 1: Y1 ENTER)Then hit ENTER

You should see this…GRAPH 16.26492733

.0907994319.6315364361

.7946926677

Body Weight vs. Backpack WeightPreviously we had estimated that a boy weighing 150 pounds would carry a pack of about 30 pounds.

Lets find out if our prediction holds.

Press TRACE arrow down (to switch from the scatterplot to the regression line—You will see the equation at the top of the screen)

Just type 150 and hit ENTER

Body Weight vs. Backpack Weight1. What is the slope of the line? Explain

what this value means in this setting. (turn to pg. 172 if you have no idea)

2. What is the y intercept? Explain what this value means in the setting.

Let’s Try Another OneHit y= and delete the equationClear your L1 and L2

Turn to pg. 152 and enter the data.

Let’s Try Another One1. Calculate the least-squares regression

line equation.

2. Graph the regression line on the scatterplot.

3. Use the regression line to make a prediction. Let’s predict the amount of natural gas Joan will use in a month with an average temperature of 30.

Natural Gas vs. Temperature1. What is the slope of the line? Explain

what this value means in this setting. (turn to pg. 172 if you have no idea)

2. What is the y intercept? Explain what this value means in the setting.

Correlation and RegressionCorrelation and regression are closely connected, even though regression requires choosing an explanatory variable and correlation does not.

Turn to pg. 177 and look at the bold headings

Ticket Out The DoorOn a 3x5 card please write you name and answer the following…

3 - things you learned today

2 - questions you still have

1- summarize the lesson in ONE sentence

HomeworkPg. 173#’s 4.28, 4.29, and 4.32