QUAT6221 LU4
QUAT6221 LU4 – Simple Linear
Regression and Correlation Analysis
Chapter 12
12.1 Intro
Regression analysis and correlation analysis are 2
statistical methods that aim to quantify the relationship
between these variables and measure the strength of
this relationship.
The scatter plot shows us:
- Correlation analysis = closeness of the scatter
points to the straight line, also shows strength
of the relationship
- Regression analysis = pattern of the scatter
points shows us the nature of the relationship
To perform these analysis, the data for both variables must be numeric.
12.2 Simple Linear Regression Analysis
Simple linear regression analysis finds a straight-line equation that represents the
relationship between the values of 2 numeric variables. x influences the outcome of y.
x is called the independent or predictor variable
y is called the dependent or response variable
Regression is calculated using:
^y =a+bx
a=
∑ y−b ∑ x
n
y = a + bx
n ∑ xy−∑ x ∑ y
b= 2
n ∑ x −(∑ x)
2
Where:
n = the number of pairs of scores
Σxy = the sum of the products of paired scores
1
, QUAT6221 LU4
Σx = the sum of x-scores
Σy = the sum of y-scores
Σx2 = the sum of x-scores squared
Example 12.1
Music electronics has recorded the number of TVs sold each week with the number of ads
placed weekly for a period of 12 weeks.
Ads 4 4 3 2 5 2 4 3 5 5 3 4
Sales 26 28 24 18 35 24 36 25 31 37 30 32
1. Find the straight line regression equation to estimate the number of flat screen TV’s
that music electronics can expect to sell each week, based on the number of ads
placed
Step 1: id dependent and independent variables
Dependent variable y = number of TV’s sold
Independent variable x = ads
Step 2: Construct a scatter plot between x and y
The scatter plot shows us
there is a positive linear relationship btwn ads placed and units sold.
Step 3: draw a regression table and calculate the totals
2
QUAT6221 LU4 – Simple Linear
Regression and Correlation Analysis
Chapter 12
12.1 Intro
Regression analysis and correlation analysis are 2
statistical methods that aim to quantify the relationship
between these variables and measure the strength of
this relationship.
The scatter plot shows us:
- Correlation analysis = closeness of the scatter
points to the straight line, also shows strength
of the relationship
- Regression analysis = pattern of the scatter
points shows us the nature of the relationship
To perform these analysis, the data for both variables must be numeric.
12.2 Simple Linear Regression Analysis
Simple linear regression analysis finds a straight-line equation that represents the
relationship between the values of 2 numeric variables. x influences the outcome of y.
x is called the independent or predictor variable
y is called the dependent or response variable
Regression is calculated using:
^y =a+bx
a=
∑ y−b ∑ x
n
y = a + bx
n ∑ xy−∑ x ∑ y
b= 2
n ∑ x −(∑ x)
2
Where:
n = the number of pairs of scores
Σxy = the sum of the products of paired scores
1
, QUAT6221 LU4
Σx = the sum of x-scores
Σy = the sum of y-scores
Σx2 = the sum of x-scores squared
Example 12.1
Music electronics has recorded the number of TVs sold each week with the number of ads
placed weekly for a period of 12 weeks.
Ads 4 4 3 2 5 2 4 3 5 5 3 4
Sales 26 28 24 18 35 24 36 25 31 37 30 32
1. Find the straight line regression equation to estimate the number of flat screen TV’s
that music electronics can expect to sell each week, based on the number of ads
placed
Step 1: id dependent and independent variables
Dependent variable y = number of TV’s sold
Independent variable x = ads
Step 2: Construct a scatter plot between x and y
The scatter plot shows us
there is a positive linear relationship btwn ads placed and units sold.
Step 3: draw a regression table and calculate the totals
2
