Given a desire of a Retail Chain management team to develop a strategy to forecasting annual sales, the following data from a random sample of existing stores has been gathered:
STORE
SQUARE FOOTAGE
ANNUAL SALES ($)
1
1726.00
3681.00
2
1642.00
3895.00
3
2816.00
6653.00
4
5555.00
9543.00
5
1292.00
3418.00
6
2208.00
5563.00
7
1313.00
3660.00
8
1102.00
2694.00
9
3151.00
5468.00
10
1516.00
2898.00
11
5161.00
10674.00
12
4567.00
7585.00
13
5841.00
11760.00
14
3008.00
4085.00
Enter the variable names as follows:
File
Next, by clicking on ‘Data View’, we can enter the data:
File
Assuming, for now, that if a relationship exists between the two variables, it is linear in nature, we can generate a simple Scatterplot (or Scatter Diagram) for the data. This is accomplished with the command sequence:
File
Which yields the following (editable) scatterplot:
File
We can generate a simple straight-line equation from the output resulting when using the Enter Command in regression:
File
File
Regression
Variables Entered/Removeda
Model
Variables Entered
Variables Removed
Method
1
Square Footageb
.
Enter
a. Dependent Variable: Annual Sales in Dollars
b. All requested variables entered.
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
1
.954a
.910
.902
$936.850
a. Predictors: (Constant), Square Footage
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
106208119.686
1
106208119.686
121.009
.000b
Residual
10532255.243
12
877687.937
Total
116740374.929
13
a. Dependent Variable: Annual Sales in Dollars
b. Predictors: (Constant), Square Footage
This is the intercept
File
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
B
Std. Error
Beta
1
(Constant)
901.247
513.023
1.757
.104
Square Footage
File1.686
.153
.954
11.000
.000
This is the slope
a. Dependent Variable: Annual Sales in Dollars
How to write up regression:
A linear regression was used to test the hypothesis that time in minutes would predict understanding. The overall model was significant in that R = .97, F(1, 222) = 579.32, p < .001. As time in minutes increased, understanding also increased.
Regression Equation(y) = a + bx
where
x and y are the variables.
b = The slope of the regression line
a = The intercept point of the regression line and the y axis.
X = First Score Y = Second Score you are predicting for
Square footage: Please solve for the following square footage:
x =
- 300
- 5000
- 6000
- 4498
- 6600
- 2200
- 3450
- 1700
- 1000
- 9000
Example: for number 1.
Y = 901.247 + 1.686(300)
901.247 + 505.8 = $1407.047
Lab 3 Assignment for Canvas upload:
For this week, please turn in a complete APA paper with all the sections as you did before including an abstract. At the end of the paper, please include all of the solved regression equation problems as I did in the first example.