1. For page 8 of chapter 9 notes, what is the regression model? O y=30.81+3.540x Oy=a+bx O y 32.67+3.142x O y=38.91+3.874x O y=38.91+3.874x O y=a+bx
1. For page 8 of chapter 9 notes, what is the regression model? O y=30.81+3.540x Oy=a+bx O y 32.67+3.142x O y=38.91+3.874x O y=38.91+3.874x O y=a+bx
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Attached a picture of the notes in reference to the question, any help appreciated. Thanks.
Transcribed Image Text:Ch 4 Linear Regression
Remember that the dots we see on a scatterplot represent actual measured values. For
these dots, the horizontal position is x and the vertical position is y. So the dot is at (x, y).
When data exhibit a linear relationship we are able to find an equation of "best fit,". On the
scatterplot this best fit line is drawn. This best fit line can be used so that for any given
value of x, we will use the best fit line (also called the regression line) to estimate a
corresponding ŷ value. We change from y to ŷ so that the reader knows that the ordered
pair was not measured, it was calculated. These values are called estimates. The formula
for the regression line (best fit line) is ŷ = a + bx.
So every (x, y) point has been measured (observed).
Every (x, y) point is found by substituting the x-value into the regression formula and
calculating ŷ. It is a prediction, or an estimate.
We find what the a and b values for the formula should be using the calculator.
Example For the striped dolphin data, the pattern was not linear. However, if we only look
at the first 60 kg of weight gain, then we do see a linear pattern. This data is shown below.
The line we see is the linear regression (best fit) line. We can use that to make predictions.
The dots on the graph are actual measurements from a sample of striped dolphins.
We will enter the striped dolphin data into the calculator, and generate a regression model.
60+
50+
40+
30+
20
10!
O 2
Data: (years, weight)
(0.4, 34), (2.4, 41), (2.6, 48),
(2.2, 52), (2.8, 51), (2.8, 61),
(3.3, 52), (4.1, 58), (6.2, 57)
Regression Model (from calculator)
Now we can predict the weight of a striped dolphin if we are told that the dolphin is
2.0 years old.
Transcribed Image Text:1. For page 8 of chapter 9 notes, what is the regression model?
O y 30.81+3.540x
y=a+bx
y=32.67+3.142x
y=38.91+3.874x
y=38.91+3.874x
O y=a+bx
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