# LR_spss

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```					                           Linear Regression in SPSS

I. SIMPLE LINEAR REGRESSION EXAMPLE
Butler’s Trucking Company is an independent trucking Company in southern
California. A major portion of Butler’s business involves deliveries throughout its
local area. To develop better work schedules, the managers want to estimate the total
daily travel time for their drivers.
Initially the managers believed that the total daily travel time would be closely
related to the number of miles traveled in making the daily deliveries. A simple
random sample of 10 driving assignments is provided in Table 1. Use SPSS to make
a scatter diagram of these deliveries (to verify that a linear relationship does exist)
and develop a regression equation expressing this relationship.

Table 1
Driving Assignment     X1=Miles Traveled       Y=Travel Time (hrs.)
1                      100                     9.3
2                      50                      4.8
3                      100                     8.9
4                      100                     6.5
5                      50                      4.2
6                      80                      6.2
7                      75                      7.4
8                      65                      6.0
9                      90                      7.6
10                     90                      6.1

SPSS Instructions

1. Click on the program SPSS 9.0 for windows. When the box appears asking you
‘what you want to do?’, click cancel.

2. Enter the values for your independent variable (x) in the first column. As you
begin entering values in this column, a heading will appear above the column
labeled var00001. Double click on the var00001 heading. A row will appear
allowing you to name your variable, format the data type (i.e. as dollars, a time),
declare the number of decimal places for expressing your values, and several
other formatting options. For this example I named the variable x.

3.    Enter your dependent variable (y) in the second column. The heading var00002
will appear above this column. Double click on var00002 to specify y (or a
descriptive name for your dependent variable) as the variable name for the data
listed in this column. Figure 1 displays your input information.

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Figure 1

4. To produce a scatter plot click on Graphs on the tool bar, and select scatter.
When the scatter plot box appear, click on simple, followed by the define tab.
You must specify the variable that you want plotted on the x, and y axes.
Highlight x in the window on your left. While x is highlighted, click the arrow to
the left of the window labeled XAxis. The label x should appear in this box.
Highlight the variable y, and click on the arrow to the left of the window labeled
YAxis.. A scatter plot will appear. You may save or print the scatter plot, and
then close the output screen by clicking file (on the tool bar) and selecting close.

5. To obtain the regression equation click on the Analyze on the tool bar. Select
Regression, and click on Linear. Inside of the Linear Regression box, you need
to specify your independent and dependent variables. Highlight x in the window
on your left. While x is highlighted, click the arrow to the left of the window
labeled Independent. The label x should appear in this box. Highlight the
variable y, and click on the arrow to the left of the window labeled Dependent..
The label y should now appear in this window.

6. Next, click on the Statistics tab on the bottom of the Linear Regression Box.
Inside of the Linear Regression: Statistics box check the boxes next to
Estimates, Model Fit, and R squared change. Then select continue. When
similar to the results shown below.

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REGRESSION
Variables Enter ed/Re m ovebd

Variables     Variables
Model     Entered       Remov ed         Method
1        Xa                       .     Enter
a. All requested variables entered.
b. Dependent Variable: Y

Model Sum m ary

Change Statistics
Adjusted         Std. Error of     R Square
Model        R         R Square       R Square         the Estimate      Change        F Change        df 1            df 2       Sig. F
1             .815 a       .664            .622              1.0018          .664         15.815              1               8
a. Predictors: (Constant), X

ANOVAb

Sum of
Model                    Squares           df              Mean Square         F           Sig.
1        Regression        15.871                  1            15.871        15.815         .004 a
Residual           8.029                  8             1.004
Total             23.900                  9
a. Predictors: (Constant), X
b. Dependent Variable: Y

a
Coe fficients

Standardi
zed
Unstandardiz ed             Coef f icien
Coef f icients                ts
Model                       B         Std. Error         Beta             t            Sig.
1        (Cons tant)        1.274          1.401                          .909           .390
X             6.783E-02            .017              .815       3.977           .004
a. Dependent Variable: Y

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Interpreting Results
1. In your second model summary table, you will find the Coefficient of
Determination, R2, and the Correlation Coefficient, R.

2. The ANOVA table gives the F statistic for testing the claim that there is no
significant relationship between your independent and dependent variables. The
sig. value is your p value. Thus you should reject the claim that there is no
significant relationship between your independent and dependent variables if p<.

3. The Coefficients box gives the b0 and b1 values for the regression equation. The
constant value is always b0. The b1value is next to your independent variable, x.

4. In the last column of the coefficient box, the p values for individual t tests for our
independent variable is given. Recall that this t test tests the claim that there is no
relationship between the independent variable and your dependent variable. Thus
you should reject the claim that there is no significant relationship between your
independent variable and dependent variable if p<.

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II. MULTIPLE REGRESSION EXAMPLE
In attempting to identify another independent variable, the managers felt that the
number of deliveries could also contribute to the total travel time. Table 2 includes the
number of deliveries for each of the random driving assignments provided in Table 1.

Table 2
Driving                  X1=Miles           X2=Number of      Y=Travel Time
Assignment               Traveled           Deliveries        (hrs.)
1                        100                4                 9.3
2                        50                 3                 4.8
3                        100                4                 8.9
4                        100                2                 6.5
5                        50                 2                 4.2
6                        80                 2                 6.2
7                        75                 3                 7.4
8                        65                 4                 6.0
9                        90                 3                 7.6
10                       90                 2                 6.1

To determine the regression equation for this scenario follow the same SPSS steps
provided for Simple Linear Regression with the following modifications:

     In Step 2, redefine x as x1, and then enter the data for x2 in another column and
name the column x2.
     In Step 3, you must specify x1 and x2 as independent variables (i.e. after placing
one of the variables in the independent box, follow the same procedure to place
the other variable in the independent box).
     Omit Step 4.

Your output for this multiple regression problem should be similar to the results shown
below.

REGRESSION

Variables Enter ed/Re m ovebd

Variables      Variables
Model       Entered       Remov ed       Method
1               a
X2, X1                   .   Enter
a. All requested variables entered.
b. Dependent Variable: Y

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Model Summ ary

Change Statistics
Adjusted    Std. Error of     R Square
Model       R       R Square      R Square    the Estimate      Change     F Change        df1             df2       Sig. F Change
1            .951 a     .904           .876          .5731          .904      32.878             2               7            .000
a. Predictors: (Constant), X2, X1

ANOVAb

Sum of
Model                        Squares           df             Mean Square         F                  Sig.
1         Regression           21.601                 2            10.800        32.878                .000 a
Residual              2.299                 7              .328
Total                23.900                 9
a. Predictors: (Constant), X2, X1
b. Dependent Variable: Y

a
Coe fficients

Standardi
zed
Unstandardiz ed             Coef f icien
Coef f icients                ts
Model                          B         Std. Error         Beta             t              Sig.
1         (Cons tant)          -.869           .952                          -.913            .392
X1              6.113E-02            .010              .735        6.182            .000
X2                    .923           .221              .496        4.176            .004
a. Dependent Variable: Y

Interpreting Results
1. In your second model summary table, you will find the Adjusted Coefficient of
Determination, Adjusted R2, and the Correlation Coefficient, R.
2. The ANOVA table gives the F statistic for testing the claim that there is no
variables. The sig. value is your p value. Thus you should reject the claim that
there is no significant relationship between your independent and dependent
variables if p<.
3. The Coefficients box gives the b0 and b1, and b2 values for the regression equation.
The constant value is always b0. The b1value is next to your x1 value, and b2 is
4. In the last column of the coefficient box, the p values for individual t tests for our
independent variables is given. Recall that this t test tests the claim that there is
no relationship between the independent variable (in the corresponding row) and
your dependent variable. Thus you should reject the claim that there is no

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significant relationship between your independent variable (in the corresponding
row) and dependent variable if p<.

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 views: 2 posted: 10/25/2011 language: English pages: 7