Suppose a researcher RW decides to give his nine participants a series of 50 photographs. He asks the participants to rank order (from 1-50) how well-dressed the individuals in the photograph were and to rank order (from 1-50) how intelligent they thought the individuals in the photograph were. One of the photographs was of a well known actor. The well-dressed rankings and the intelligence rankings for this one photo are as follows.
WELL-DRESSED INTELLIGENT
14 12
35 39
16 17
41 43
39 40
25 21
26 27
11 9
24 25
RW performs a simple linear regression (with WELL DRESSED as the Independent Variable and INTELLIGENT as the Dependent Variable) and obtains the following results.
Model Summary |
||||
Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
1 |
.988a |
.975 |
.972 |
2.10093 |
a. Predictors: (Constant), welldressed |
ANOVAa |
||||||
Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
1 |
Regression |
1215.992 |
1 |
1215.992 |
275.492 |
.000b |
Residual |
30.897 |
7 |
4.414 |
|||
Total |
1246.889 |
8 |
||||
a. Dependent Variable: intelligent |
||||||
b. Predictors: (Constant), welldressed |
Coefficientsa |
||||||
Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
||
B |
Std. Error |
Beta |
||||
1 |
(Constant) |
-3.180 |
1.886 |
-1.686 |
.136 |
|
welldressed |
1.133 |
.068 |
.988 |
16.598 |
.000 |
|
a. Dependent Variable: intelligent |
From these results, he concludes
1. that being well dressed causes people to view you as intelligent.
2. that the linear relationship between well-dressed ratings and intelligence ranks for the photos is Intelligence=-3.180(Well Dressed) + 1.133.
3. that the null hypothesis (b=0) has a probability =.000
4. that since it is desirable to get an R2=1, it may be necessary to add more Independent Variables to the analysis.
5. that with this type of analysis one doesn’t have to worry about being overly influenced by extreme values.
Your task is to answer the following about the above project.
Do you see any problems with the design of the study, the data analysis run, or the results reported?
Are there analyses that should have been run that weren’t? What would you have done? Why?
Do you see any errors in the conclusions reached? If so, what should have been (or should not have been) concluded?
If you feel that other alternative statistical analyses should have been performed, then do them. If you do alternative analyses include any results you have obtained
Answer:
Regression model is :
Intelligents =
Intelligents = - 3.180 + 1.133 * welldressed
the intelligents predicted to 1.133 welldressed incresed by per one unit of intelligents.
The intelligents -3.180 decresed by the one unit of intelligents. IF welldressed zero so mean of intelligents is -3.180
97.5% indicates that the model explains all the variability of the intelligents data around its mean.
This model is very good fit for the given data set.
Regession sum of square is significant of 0.05 level of alpha
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