regression

1. Regression Analysis
 Explain the impact of one variable on another
Independent variable:
the variable used to explain
the dependent variable
Dependent
variable
the variable you
wish to explain
is used to
x-axis
y-axis
Simple Linear
independent
Annual Salary vs. Education
$0
$20,000
$40,000
$60,000
$80,000
$100,000
$120,000
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Annual salary
Years of Education (past high school)
?

2. Regression Analysis
Independent variable
Dependent variable
is also used to
x-axis
y-axis
Simple Linear
Quantify linear relationships
…develop an equation for the…
Y = mX + b
value of Y when X = 0
change in Y relative to a change in X
Y = b1X + b0
slope
intercept
The purpose of regression analysis is calculate estimates of the slope and intercept.

3. Regression Analysis
Independent variable
Dependent variable
is also used to
x-axis
y-axis
Simple Linear
Quantify linear relationships
…develop an equation for the…
Y = mX + b
value of Y when X = 0
change in Y relative to a change in X
Y = b1X + b0
slope
intercept
The purpose of regression analysis is calculate estimates of the slope and intercept.
=INTERCEPT(y-range, x-range)
=SLOPE(y-range, x-range)
using LEAST SQUARES ESTIMATION

4. Linear Regression Example
Scatterplot
 House price model: scatter plot
0
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Square Feet
House Price ($1000s)
(1) Describe
the
relationship…
r = 0.762

5. House price model: scatter plot and regression line
y = 0.1098x + 98.248
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Price in $1000s
sqft
Selling Price vs. Square Feet
trendline
(2) Model the Data…
Calculate the regression coefficients
and interpret
b0 is the estimated mean value of Y when the value of X is 0
(if X = 0 is in the range of observed X values)
Because the square footage of the house cannot be 0, the Y intercept has no practical application.
slope
intercept

6. House price model: scatter plot and regression line
y = 0.1098x + 98.248
0
50
100
150
200
250
300
350
400
450
0
500
1000
1500
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2500
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Price in $1000s
sqft
Selling Price vs. Square Feet
trendline
(2) Model the Data…
Calculate the regression coefficients
and interpret
b1 measures the mean change in the average value of Y as a result of a one-unit change in X The mean value of a house increases by 0.1098($1000) = $109.80, on average, for each additional one square foot of size
slope
intercept

7. y = 0.1098x + 98.248 R² = 0.5808
0
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Price in $1000s
sqft
Selling Price vs. Square Feet
(3) Evaluate the Model…
Calculate R2
58% of the variability in the PRICE of a home is exaplined by using the SIZE of the home.

8. Standard Error of Estimate
 The standard deviation of the
observations around the
regression line.
When predicting, this is the stdev
of the predictions
(3) Evaluate
the Model…
Calculate R2 and std error

9. y = 0.1098x + 98.248 R² = 0.5808
0
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100
150
200
250
300
350
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450
0
500
1000
1500
2000
2500
3000
Price in $1000s
sqft
Selling Price vs. Square Feet
(3) Evaluate the Model…
Calculate R2 and std error
SYX=41.33