Different Ways to Look at Slope

1.3 Using Linear Equations

So far we’ve covered how to take data and generate an equation by using the slope intercept form, finding the slope, and using an ordered pair to find the y intercept. Now, we need to start making use of the equations we find.

Different ways to look at slope –

From your text:

In the book’s example about blood pressure (which I’m sure you read in detail), the initial value for slope that was determined from the data was

Slope = 0.69.

Rewriting the slope as a fraction and attaching units, it looks like:

The point is, just because the slope turns out to be some weird number, doesn’t necessarily me you need to leave it that way.

Least Squares Regression

Meet your new best friend: “least squares regression”

This is a little tool, actually is a GREAT TERRIFIC tool you will be using on your calculator. This application is going to save you a lot of work and time. It’s also going to give us equations that are generally much more accurate than what we can do by hand. Just remember, garbage in garbage out.

Least squares regression on your calculator, gives us the best possible fit for a trend line, given a set of data. This takes the guessing out of where you would place the trend line if you were doing it by hand.

Front your text:

The concept is simple; consider the 5 points in the figure and the vertical distance each is away from the line. The distances above the line are positive and below the line are negative. The easiest method to find the best trend line is to square the distances to remove the negatives, and then add them to find the least sum possible, hence the name least squares regression.

How to use your calculator. This is one of the videos in your list

(5. Regression and Correlation).

Example Problem #2 from text – A1 A2

Homework: 1, 3, 5, 7, 8 – Your work should be as demonstrated in class.

Sample Problem 1.3.4

A tree’s diameter and volume are naturally related.

Round slopes and y-intercepts to 3 decimal places

a)  Find the equation for the trend line using the regression feature of your graphing calculator.

b)  Use your regression equation to predict the volume of a 5.5 cm diameter tree, accurate to 1 decimal place.

c)  Use your regression equation to predict the diameter a tree would need to have a 500 m3 volume, accurate to 2 decimal places.

Solutions:

a) After entering the data in two lists, use the linear regression function to generate the equation.

b) c)