DEPARTMENT OF PSYCHOLOGY

PSY2005 Statistics and Research Methods: Quantitative data analysis component

Introduction to multiple regression: examples

1. Use Minitab to carry out the multiple regression on depression scores that was used as an example in the lecture. Check that you get the same result as was reported then. The data and results are reproduced at the end of this examples sheet.
2. Use Minitab's HELP facility to find out how to use the READ command to read data into Minitab from a text file.
3. The Singer file /singer1/eps/psybin/stats/teengamb.DAT contains, for each of 47 teenagers, the following information:
• respondent number
• gender (0=male, 1=female)
• status (arbitrary scale based on parents' occupation. Higher numbers => higher status)
• income (pocket money+earnings) in pounds/wk
• verbal intelligence (number of words out of 12 correctly defined)
• estimate (from questionnaire answers) of expenditure on all forms of gambling, in pounds/yr

Each line of the file contains all 6 data items for a single person. These are real data, collected during an undergraduate project some years ago, and since published (Ide-Smith & Lea, 1988, Journal of Gambling Behavior, 4, 110-118). Set up your Minitab worksheet with columns with appropriate names, and read these data into it using READ. Note that you don't need to type the file extension (.DAT) because this is the default for READ, but if you do type it, you must use CAPITALS. The rest of the filename must be typed in lower case.

4. Use Minitab's DESCRIBE command to get an overview of these data.
5. Use multiple regression to see whether gambling can be predicted from status, income, and verbal intelligence.
6. How good is the prediction?
7. Which variables have significant effects?
8. Give a description in words, as precise as you can make it, of the most significant effect.
9. Use HELP to remind yourself what Minitab's TWOT command does and how it works.
10. Use TWOT to find out how gambling seems to have been affected by gender in this sample when all other variables are ignored.
11. Repeat the multiple regression, but this time include gender as a predictor variable in the REGRESS command. This will allow you to assess the effect of gender with the other variables taken into account. Compare the results with those you got when you used TWOT.
12. Using this second regression equation, predict how much money you would have been expected to spend on gambling when you were 14. Is the prediction accurate? If not, why do you think it fails?
13. How would you have analysed these data if you hadn't had multiple regression available?

The published article is in the library, but you won't get quite the same results as we did, because I've cut out the data from some respondents who would have given you problems.

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Worked example of an elementary multiple regression

MTB > set c1
DATA> 74 82 15 23 35 54 12 28 66 43 55 31 83 29 53 32
DATA> end
MTB > set c2
DATA> 120 55 350 210 185 110 730 150 61 175 121 225 45 325 171 103
DATA> end
MTB > set c3
DATA> 0 0 1 0 0 1 1 0 1 1 1 0 1 0 0 1
DATA> end
MTB > set c4
DATA> 33 28 47 55 32 63 59 68 27 32 42 51 47 33 51 20
DATA> end
MTB > name c1 'depress'
MTB > name c2 'income'
MTB > name c3 'm0f1'
MTB > name c4 'age'

MTB > regress c1 3 c2-c4


The regression equation is
depress = 68.3 0.0934 income + 3.31 m0f1 - 0.162 age




Predictor       Coef       Stdev    t-ratio       p
Constant       68.28       15.44       4.42    0.001
income      -0.09336     0.02937      -3.18    0.008
m0f1           3.306       8.942       0.37    0.718
age          -0.1617      0.3436      -0.47    0.646

s = 17.70       R= 52.0%     R= 39.9%


Analysis of Variance

SOURCE       DF          SS          MS         F        p
Regression    3      4065.4      1355.1      4.32    0.028
Error        12      3760.0       313.3
Total        15      7825.4

SOURCE       DF      SEQ SS
income        1      3940.5
m0f1          1        55.5
age           1        69.4

Continue? y
Unusual Observations
Obs.  income   depress       Fit Stdev.Fit  Residual   St.Resid
  7      730     12.00     -6.10     15.57     18.10      2.15RX

R denotes an obs. with a large st. resid.
X denotes an obs. whose X value gives it large influence.

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(access count since 1st February 1997).
Document revised 27th August 1997

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