Question:
Provide appropriate variable labels, values labels, and scaling indications to the variables.
Answer:
Data handling
Relevant file of MS Excel and SPSS have been provided
Descriptive
|
Statistics
|
|
Age
|
|
N
|
Valid
|
24
|
|
Missing
|
0
|
|
Mean
|
22.96
|
|
Median
|
21.00
|
|
Mode
|
21
|
|
Std. Deviation
|
4.563
|
|
Variance
|
20.824
|
|
Statistics
|
|
Exam Marks
|
|
N
|
Valid
|
24
|
|
Missing
|
0
|
|
Mean
|
82.00
|
|
Median
|
81.00
|
|
Mode
|
75a
|
|
Std. Deviation
|
8.011
|
|
Variance
|
64.174
|
|
Statistics
|
|
Paper Marks
|
|
N
|
Valid
|
24
|
|
Missing
|
0
|
|
Mean
|
80.33
|
|
Median
|
81.00
|
|
Mode
|
75a
|
|
Std. Deviation
|
10.277
|
|
Variance
|
105.623
|
|
Statistics
|
|
IQ
|
|
N
|
Valid
|
24
|
|
Missing
|
0
|
|
Mean
|
101.08
|
|
Median
|
99.00
|
|
Mode
|
99
|
|
Std. Deviation
|
25.082
|
|
Variance
|
629.123
|
Recoding has been performed in the SPSS data input file.
|
Sex
|
|
|
Frequency
|
Percent
|
Valid Percent
|
Cumulative Percent
|
|
Valid
|
M
|
11
|
45.8
|
45.8
|
45.8
|
|
F
|
13
|
54.2
|
54.2
|
100.0
|
|
Total
|
24
|
100.0
|
100.0
|
|
|
Year In College
|
|
|
Frequency
|
Percent
|
Valid Percent
|
Cumulative Percent
|
|
Valid
|
1
|
5
|
20.8
|
20.8
|
20.8
|
|
2
|
6
|
25.0
|
25.0
|
45.8
|
|
3
|
9
|
37.5
|
37.5
|
83.3
|
|
4
|
4
|
16.7
|
16.7
|
100.0
|
|
Total
|
24
|
100.0
|
100.0
|
|
From the histogram diagram above it can be concluded that the IQ and Exam marks are positively correlated. As the level of IQ increases the marks obtained in the exams also increase.
The scatter plot depicts a spurious correlation between the dependent and independent variables and as a result it can be stated that there exists no relationship between these variables.
|
Statistics
|
|
IQ
|
|
M
|
N
|
Valid
|
11
|
|
Missing
|
0
|
|
Mean
|
101.18
|
|
F
|
N
|
Valid
|
13
|
|
Missing
|
0
|
|
Mean
|
101.00
|
|
Year In College * IQDum Crosstabulation
|
|
Count
|
|
|
IQDum
|
Total
|
|
Others
|
>=100
|
|
Year In College
|
Freshman
|
4
|
1
|
5
|
|
Sophomore
|
3
|
3
|
6
|
|
Junior
|
5
|
4
|
9
|
|
Senior
|
2
|
2
|
4
|
|
Total
|
14
|
10
|
24
|
|
One-Sample Test
|
|
|
Test Value = 75
|
|
t
|
df
|
Sig. (2-tailed)
|
Mean Difference
|
95% Confidence Interval of the Difference
|
|
Lower
|
Upper
|
|
Exam Marks
|
4.281
|
23
|
.000
|
7.000
|
3.62
|
10.38
|
As the value of t at 95% confidence interval is higher than that of the tabulated value, the null hypothesis is rejected. Hence the exam grades are not significantly higher than 75.
|
Independent Samples Test
|
|
|
Levene’s Test for Equality of Variances
|
t-test for Equality of Means
|
|
F
|
Sig.
|
t
|
df
|
Sig. (2-tailed)
|
Mean Difference
|
Std. Error Difference
|
95% Confidence Interval of the Difference
|
|
Lower
|
Upper
|
|
Exam Marks
|
Equal variances assumed
|
.703
|
.411
|
1.763
|
22
|
.092
|
5.538
|
3.141
|
-.976
|
12.052
|
|
Equal variances not assumed
|
|
|
1.790
|
22.000
|
.087
|
5.538
|
3.094
|
-.878
|
11.955
|
|
Paired Samples Statistics
|
|
|
Mean
|
N
|
Std. Deviation
|
Std. Error Mean
|
|
Pair 1
|
Exam Marks
|
82.00
|
24
|
8.011
|
1.635
|
|
Paper Marks
|
80.33
|
24
|
10.277
|
2.098
|
|
Paired Samples Correlations
|
|
|
N
|
Correlation
|
Sig.
|
|
Pair 1
|
Exam Marks & Paper Marks
|
24
|
.626
|
.001
|
|
Paired Samples Test
|
|
|
Paired Differences
|
t
|
df
|
Sig. (2-tailed)
|
|
Mean
|
Std. Deviation
|
Std. Error Mean
|
95% Confidence Interval of the Difference
|
|
Lower
|
Upper
|
|
Pair 1
|
Exam Marks – Paper Marks
|
1.667
|
8.165
|
1.667
|
-1.781
|
5.114
|
1.000
|
23
|
.328
|
|
Statistics
|
|
Paper Marks
|
|
Freshman
|
N
|
Valid
|
5
|
|
Missing
|
0
|
|
Mean
|
79.40
|
|
Sophomore
|
N
|
Valid
|
6
|
|
Missing
|
0
|
|
Mean
|
78.00
|
|
Junior
|
N
|
Valid
|
9
|
|
Missing
|
0
|
|
Mean
|
81.33
|
|
Senior
|
N
|
Valid
|
4
|
|
Missing
|
0
|
|
Mean
|
82.75
|
The mean value depicts that there is not a significance difference between the mean values of the Paper grades of the four groups in the college.
|
Correlations
|
|
|
Age
|
Exam Marks
|
Paper Marks
|
IQ
|
|
Age
|
Pearson Correlation
|
1
|
.222
|
.297
|
.182
|
|
Sig. (2-tailed)
|
|
.296
|
.159
|
.395
|
|
N
|
24
|
24
|
24
|
24
|
|
Exam Marks
|
Pearson Correlation
|
.222
|
1
|
.626**
|
.584**
|
|
Sig. (2-tailed)
|
.296
|
|
.001
|
.003
|
|
N
|
24
|
24
|
24
|
24
|
|
Paper Marks
|
Pearson Correlation
|
.297
|
.626**
|
1
|
.749**
|
|
Sig. (2-tailed)
|
.159
|
.001
|
|
.000
|
|
N
|
24
|
24
|
24
|
24
|
|
IQ
|
Pearson Correlation
|
.182
|
.584**
|
.749**
|
1
|
|
Sig. (2-tailed)
|
.395
|
.003
|
.000
|
|
|
N
|
24
|
24
|
24
|
24
|
|
**. Correlation is significant at the 0.01 level (2-tailed).
|
The correlation matrix depicts the fact that IQ and Paper marks depict a good correlation which means with higher IQ people will be able to obtain higher paper marks. In the context of paper marks and IQ as well the scenario is same. On an added notion IQ and age also possess higher value of correlation coefficient. The rest of the coefficients are positive but the values are low and hence cannot be considered to be a better result there might be a little dependence of one variable on the other.
|
Variables Entered/Removeda
|
|
Model
|
Variables Entered
|
Variables Removed
|
Method
|
|
1
|
IQ, Sex, Ageb
|
.
|
Enter
|
|
a. Dependent Variable: Paper Marks
|
|
b. All requested variables entered.
|
|
Model Summary
|
|
|
Model
|
R
|
R Square
|
Adjusted R Square
|
Std. Error of the Estimate
|
|
|
1
|
.790a
|
.624
|
.568
|
6.758
|
|
|
a. Predictors: (Constant), IQ, Sex, Age
|
|
|
ANOVAa
|
|
|
Model
|
Sum of Squares
|
df
|
Mean Square
|
F
|
Sig.
|
|
|
1
|
Regression
|
1515.889
|
3
|
505.296
|
11.064
|
.000b
|
|
|
Residual
|
913.445
|
20
|
45.672
|
|
|
|
|
Total
|
2429.333
|
23
|
|
|
|
|
|
a. Dependent Variable: Paper Marks
|
|
|
b. Predictors: (Constant), IQ, Sex, Age
|
|
|
Coefficientsa
|
|
Model
|
Unstandardized Coefficients
|
Standardized Coefficients
|
t
|
Sig.
|
|
B
|
Std. Error
|
Beta
|
|
1
|
(Constant)
|
43.328
|
8.548
|
|
5.069
|
.000
|
|
Age
|
.412
|
.315
|
.183
|
1.307
|
.206
|
|
Sex
|
-3.841
|
2.779
|
-.190
|
-1.382
|
.182
|
|
IQ
|
.293
|
.057
|
.715
|
5.128
|
.000
|
|
a. Dependent Variable: Paper Marks
|
