Data Management Investigation - Assignment Example

Data was collected on the following variables:

• Places where one studies-distracting or quite
• Time of day a person studies – day or night
• Number of hours a person slept
• Exam score
• Age
• Food quality – on a scale of 1-5 based on the quality of food

Summary Statistics

The graph for the type of environment shows that 72 percent of students studied in a quiet environment as compared to 28 percent who studied in a distracting environment.

For the variable on the time of study, the histogram shows that 61% of respondents studied at night while the remaining 39% studied during the day.  Studying until late in the night can have an impact on the results as a student takes exam while the brain is fatigued and is not functioning at its optimum.

               The histogram on the quality of food shows that a significant proportion of the sampled students had quality food. The categories were obtained as follows:

• Category 1- Food consisting of one nutrient
• Category 2- Food consisting of two nutrients
• Category 3- Food consisting of three nutrients
• Category 4- Food consisting of all nutrients and fluid accompaniments (water/juice)
• Category 5- Food consisting of all nutrients and a fruit accompaniment

Column1

Mean

6.54

Median

6

Mode

6

Standard Deviation

1.351542

Sample Variance

1.826667

Count

100

The histogram and summary statistics for number of hours slept is shown above. From the results, we see that the average hours of sleep for grade 12 students are 6.5 hours with a standard deviation of 1.35. It has been recommended that students should sleep for at least 6 hours to maximize their cognitive ability.

Column1

Mean

17.62

Median

18

Mode

18

Standard Deviation

1.108097

Sample Variance

1.227879

Count

100

Correlation

Age

Hours slept

Age

1

Hours slept

-0.72491

1

A scatterplot of age versus hours slept shows a negative correlation, i.e. older persons tend to sleep fewer hours as compared to younger ones. Indeed, the results from the scatterplot are further confirmed by results from the correlation table. The correlation is -0.725 implying a negative correlation between the two variables.

Correlation (Hours slept and Exam score)

Hours Slept

Exam score

Hours Slept

1

Exam Score

0.616685

1

A plot of exam score against hours slept shows a positive correlation between the two variables. Further analysis through correlation shows a value of 0.617. Consequently, the preliminary analysis supports the null hypothesis that academic performance is positively related with the number of sleep hours. Further analysis through regression is needed to build confidence in this hypothesis.

Regression

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.624392

R Square

0.389865

Adjusted R Square

0.370799

Standard Error

9.282865

Observations

100

ANOVA

df

SS

MS

F

Significance F

Regression

3

5285.968

1761.989

20.44745

2.51E-10

Residual

96

8272.472

86.17158

Total

99

13558.44

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

47.61781

26.84476

1.773822

0.079263

-5.66861

100.9042

-5.66861

100.9042

Hours_slept

4.478944

1.002367

4.468369

2.16E-05

2.489262

6.468626

2.489262

6.468626

Age

-1.45474

1.222369

-1.1901

0.236942

-3.88112

0.971641

-3.88112

0.971641

Food Quality

-0.27738

0.981166

-0.28271

0.77801

-2.22498

1.670216

-2.22498

1.670216

Final analysis of the data involved regression modeling using exam scores as the dependent variable and hours slept, age and food quality as the independent variables. The regression equation can be stated as follows:

Exam score = 47.62 + 4.479 (hours slept) – 1.455 (age) – 0.277 (Food quality)

From the equation, it is observed that the intercept for the number of hours slept is positive implying that hours of sleep positively impacts test scores. This can be stated as follows: a unit increase in hours slept results into a 4.479 unit increase in examination scores. However, age and food quality have a negative impact on test scores. We can conclude that younger persons outperform older persons in the same class.

            From the graphical and regression analyses conducted in this paper, we can conclude that the higher the number of sleeping hours, the better the test scores. However, this generalization must be applied with caution as success in exams is affected by numerous factors. Besides, the number of hours slept cannot be increased to infinity for best test score results. There has to be a limit on this variable.