Score GPA Hours Absences Gender 79 3.35 1.5 Female 73 2.75 3.5 Female 83 3.04 6.5 1 Male 73 2.53 3.0 Female 88 2.92 6.0 1 Male 75 2.99 2.0 Male 87 3.89 7.5 4 Male Female 3.0 4.0 76 2.98 77 2.25 Female 84 3.54 4.0 Male 2.5 2 Female 2.84 2.60 74 74 2.5 Male
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
A business statistics professor would like to develop a regression model to predict the final exam scores for students based on their current GPAs, the number of hours they studied for the exam, the number of times they were absent during the semester, and their genders. The data for these variables are given in the accompanying table at the bottom of this page.
a) Using Excel, construct a regression model using all of the independent variables. Create the dummy variable Gen, which equals 1 for a male and 0 for a female student ( this assignment is arbitrary)
complete the regression equation for the model below, where y= Score, x1= GPA, x2= Hours, x3= Absenses, and x4= Gen.
y= (__) + (__)x1 + (__)x2 + (__)x3 + (__)x4
b) Test the significance of the overall regression model using a= 0.10.
c) interpret the meaning of the regression coefficient for the dummy variable.
d) using the p-values, identify which independent variables are significant with a= 0.10.
e) construct a regression model using only the significant variables found in part c and predict the average exam score for a student who studied 3.5 hours for the exam, missed three classes during the semester, has a current GPA of 3.89, and is female.
| Score | GPA | Hours | Absences | Gender |
| 79 | 3.35 | 1.5 | 0 | Female |
| 73 | 2.75 | 3.5 | 6 | Female |
| 83 | 3.04 | 6.5 | 1 | Male |
| 73 | 2.53 | 3.0 | 0 | Female |
| 88 | 2.92 | 6.0 | 1 | Male |
| 75 | 2.99 | 2.0 | 3 | Male |
| 87 | 3.89 | 7.5 | 4 | Male |
| 76 | 2.98 | 3.0 | 3 | Female |
| 77 | 2.25 | 4.0 | 3 | Female |
| 84 | 3.54 | 4.0 | 0 | Male |
| 74 | 2.84 | 2.5 | 2 | Female |
| 74 | 2.60 | 2.5 | 1 | Male |
![### Regression Model Development for Predicting Exam Scores
A business statistics professor seeks to develop a regression model to predict students' final exam scores. This prediction is based on:
- Current GPA
- Number of study hours for the exam
- Number of absences during the semester
- Gender
The data for these variables are included in an accompanying table.
#### Task Instructions:
1. **View the Data Table:**
- Click the icon to access the data table.
2. **Regression Model Construction Using Excel:**
- Develop a regression model including all independent variables.
- Create a dummy variable for Gender (Gen), where:
- `1` represents male
- `0` represents female
- Note: This assignment of value is arbitrary.
3. **Complete the Regression Equation:**
- Use the model:
\[
\hat{y} = \text{constant} + \text{b}_1 \times x_1 + \text{b}_2 \times x_2 + \text{b}_3 \times x_3 + \text{b}_4 \times x_4
\]
- Where:
- \( y \) = Score
- \( x_1 \) = GPA
- \( x_2 \) = Hours
- \( x_3 \) = Absences
- \( x_4 \) = Gen
- Round each coefficient to two decimal places as needed.
4. **Submission:**
- Enter your solution in the provided fields and click "Check Answer."
This exercise assists in understanding how multiple variables can be used in regression analysis to predict outcomes, emphasizing practical application using statistical software.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F276c86e6-d17b-4457-8be2-42dfe19eb373%2F3906440d-9f9f-4a81-9543-c1d288ab7bd9%2Ft2fdpd8_processed.jpeg&w=3840&q=75)
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