Simple Linear Regression Equation (Line of Best Fit / Prediction line)
?
̂ = β
̂
0
+ β
̂
1
?
where
?
̂
= dependent variable (the predicted value)
?
= independent variable (your known value)
β
̂
0
= y-intercept
β
̂
1
= slope
Independent
variable
X
Dependent
variable
Y
Amount of shelf space
Monthly
Sales
Line of Best Fit

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Example 3
The 759 store’s goal is to forecast annual sales for all new stores, based on store si
ze. To examine
the relationship between the store size in square feet and its annual sales, a sample of 14 stores
was selected. The following table summarizes the results for these 14 stores, which are stored in
the file
site
.xls
Step 1)
Construct a scatter plot.
Observe the increasing relationship between square feet (X) and annual sales (Y). As the size of
the store increases, annual sales increase approximately as a straight line. Thus, you can assume
that a straight line provides a useful mathematical model of this relationship. Now you need to
determine the specific straight line that is the best fit to these data.

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Step 2)
Find the line of best fit
Click
Analyze > Regression > Linear...
Descriptive Statistics
Mean
Std. Deviation
N
Annual Sales
5.843
2.9994
14
Square Feet
2.921
1.7080
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Correlations
Annual Sales
Square Feet
Pearson Correlation
Annual Sales
1.000
.951
Square Feet
.951
1.000
Sig. (1-tailed)
Annual Sales
.
.000
Square Feet
.000
.
N
Annual Sales
14
14
Square Feet
14
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