MM207 Unit 5 Discussion: Analysis of Study Hours & Test Scores Correlation

Student Name

Purdue University Global

MM207 Statistics

Prof. Name:

Date

Relationship Between Study Hours and Test Scores

The scatter plot demonstrates a strong positive linear relationship between study hours and test scores. As the number of hours spent studying increases, test scores also tend to increase. This relationship is supported by both the visual trend in the scatter plot and the calculated correlation coefficient (r = 0.774), indicating that students who study more generally achieve higher test scores.

Variables Used in the Scatter Plot

The scatter plot was created using the Hours of Study and Test Scores dataset from the Math for Teachers website. The variables include:

Independent Variable (X-axis): Study Hours
Dependent Variable (Y-axis): Test Scores

Data Elements Included

The scatter plot contains the following data elements:

Number of study hours plotted on the X-axis
Test scores plotted on the Y-axis
Labels for both axes
Individual data points representing each observation
Test score values displayed above each corresponding data point

Interpretation of the Scatter Plot

The visual pattern of the scatter plot shows that as study hours increase, test scores also increase. Most data points follow an upward trend from left to right, indicating a positive linear association between the two variables.

Although some variation exists among individual observations, the overall distribution suggests that increased study time is associated with improved academic performance.

Correlation Analysis

The calculated Pearson correlation coefficient (r) for the dataset is:

r = 0.774084839

A correlation coefficient of 0.774 indicates a strong positive correlation. Because the value is close to +1, it suggests that higher study hours are strongly associated with higher test scores.

The calculated correlation coefficient also exceeds the reported critical values of 0.514 (α = 0.05) and 0.641 (α = 0.01). Therefore, the relationship between study hours and test scores is statistically significant, providing evidence of a meaningful positive linear relationship between the variables.

Key Findings

Students who study for more hours generally achieve higher test scores.
The scatter plot displays a clear upward trend, indicating a positive linear relationship.
The Pearson correlation coefficient (r = 0.774) represents a strong positive association.
The correlation is statistically significant because it exceeds the critical values at both the 0.05 and 0.01 significance levels.
The visual pattern and statistical analysis consistently support the conclusion that increased study time is associated with better academic performance.

A Pearson correlation coefficient of 0.774 indicates a strong positive relationship between study hours and test scores, meaning that increases in study time are generally associated with higher academic performance.

Scatter plots are commonly used to visualize relationships between two quantitative variables, while the Pearson correlation coefficient measures the strength and direction of a linear relationship.

FAQs

What does the scatter plot show?

The scatter plot shows a strong positive linear relationship between study hours and test scores. Students who spend more time studying generally earn higher test scores.

What is the independent variable?

The independent variable is study hours, which is plotted on the X-axis.

What is the dependent variable?

The dependent variable is test scores, which is plotted on the Y-axis because it is expected to change based on the number of study hours.

What does a correlation coefficient of 0.774 mean?

A correlation coefficient of 0.774 indicates a strong positive linear relationship. As one variable increases, the other tends to increase as well.

Is the relationship statistically significant?

Yes. Since the calculated correlation coefficient (r = 0.774) is greater than the critical values at both the 0.05 and 0.01 significance levels, the relationship is considered statistically significant.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). https://apastyle.apa.org/

Lane, D. M. (n.d.). Online Statistics Education: Correlation. Rice University. https://onlinestatbook.com/