Document Sample

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. 1 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 you return to the Linear Regression Box, click ok. Your results should look similar to the results shown below. 2 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 3 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<. 4 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 5 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 significant relationship between your all of 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, and b2 values for the regression equation. The constant value is always b0. The b1value is next to your x1 value, and b2 is next to your x2 value. 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 6 significant relationship between your independent variable (in the corresponding row) and dependent variable if p<. 7

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 2 |

posted: | 10/25/2011 |

language: | English |

pages: | 7 |

OTHER DOCS BY panniuniu

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.