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Algebra Review, Linear Regression, Correlation Coefficient | STAT 101, Study notes of Statistics

Iowa State University (ISU)Statistics

Material Type: Notes; Class: PRIN OF STATISTICS; Subject: STATISTICS; University: Iowa State University; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

koofers-user-hxk
koofers-user-hxk 🇺🇸

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Stat 101L: Lecture 12
1
1
Algebra Review
The equation of a straight line
y= mx + b
–m is the slope – the change in y
over the change in x– or rise
over run.
–b is the y-intercept – the value
where the line cuts the yaxis.
2
-5-4-3-2-1012345
-15
-10
-5
0
5
10
15
x
y
y = 3x + 2
3
Review
y= 3x+ 2
–x= 0 y= 2 (y-intercept)
–x= 3 y= 11
–Change in y (+9) divided by the
change in x (+3) gives the slope,
3.
pf3
pf4
pf5

Partial preview of the text

Download Algebra Review, Linear Regression, Correlation Coefficient | STAT 101 and more Study notes Statistics in PDF only on Docsity!

1

Algebra Review

The equation of a straight line

y = m x + b

  • m is the slope – the change in y over the change in x – or rise over run.
  • b is the y -intercept – the value where the line cuts the y axis.

2

-5 -4 -3 -2 -1 0 1 2 3 4 5

0

5

10

15

x

y

y = 3x + 2

3

Review

y = 3 x + 2

  • x = 0 y = 2 (y-intercept)
  • x = 3 y = 11
  • Change in y (+9) divided by the change in x (+3) gives the slope,

4

Linear Regression

Example: Tar (mg) and

nicotine (mg) in cigarettes.

  • y , Response: Nicotine (mg).
  • x , Explanatory: Tar (mg).
  • Cases: 25 brands of cigarettes.

5

Correlation Coefficient

Tar and nicotine

r = 0.

∑

n

z z

r

x y

6

Linear Regression

There is a strong positive linear

association between tar and

nicotine.

What is the equation of the line

that models the relationship

between tar and nicotine?

10

Line of “Best Fit”

There are lots of straight lines

that go through the data.

The line of “best fit” is the line

for which the sum of squared

residuals is the smallest – the

least squares line.

11

Line of “Best Fit”

y ˆ = b 0 + b 1 x

Least squares slope:

intercept:

x

y s

s b 1 = r

b 0 (^) = y − b 1 x

12

Tar, x Nicotine, y

  1. 636 mg

  2. 92 mg

r

s

x

x^0.^2812 mg

  1. 908 mg =

s y

y

Summary of the Data

13

Least Squares Estimates

y x

b

b

0

1

14

Interpretations

Slope – for every 1 mg increase in tar, the nicotine content increases, on average, 0.058 mg.

Intercept – there is not a reasonable interpretation of the intercept in this context because one wouldn’t see a cigarette with 0 mg of tar.

15

0 5 10 15 20 25

Tar (mg)

Nicotine (mg)

Nicotine Content vs. Tar Content

Predicted Nicotine = 0.217 + 0.058Tar