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Answer :
To find the regression equation for the provided data set, where [tex]$y$[/tex] is the final grade in a math class and [tex]$x$[/tex] is the average number of hours spent on math each week, follow these steps:
### Step 1: Calculate the Regression Equation
The regression equation is of the form:
[tex]\[ y = m \cdot x + b \][/tex]
Where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line.
For the given data:
- Hours per week ([tex]$x$[/tex]): [5, 9, 11, 13, 14, 14, 14, 15, 17, 19]
- Grades ([tex]$y$[/tex]): [46, 64.6, 79.4, 77.2, 78.6, 85.6, 77.6, 97, 97.8, 100]
From the analysis, it was found that:
- The slope [tex]\( m \approx 3.93 \)[/tex]
- The intercept [tex]\( b \approx 28.91 \)[/tex]
So, the regression equation is:
[tex]\[ y = 3.93 \cdot x + 28.91 \][/tex]
### Step 2: Predict the Final Grade
Now, we want to predict the final grade for a student who spends an average of 13 hours per week on math. Using the regression equation:
Substitute [tex]\( x = 13 \)[/tex] into the equation:
[tex]\[ y = 3.93 \cdot 13 + 28.91 \][/tex]
Calculate the value:
[tex]\[ y = 51.09 + 28.91 \][/tex]
[tex]\[ y \approx 80.0 \][/tex]
Therefore, the predicted final grade when a student spends an average of 13 hours each week on math is approximately 80.0 when rounded to 1 decimal place.
### Step 1: Calculate the Regression Equation
The regression equation is of the form:
[tex]\[ y = m \cdot x + b \][/tex]
Where:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\( b \)[/tex] is the y-intercept of the line.
For the given data:
- Hours per week ([tex]$x$[/tex]): [5, 9, 11, 13, 14, 14, 14, 15, 17, 19]
- Grades ([tex]$y$[/tex]): [46, 64.6, 79.4, 77.2, 78.6, 85.6, 77.6, 97, 97.8, 100]
From the analysis, it was found that:
- The slope [tex]\( m \approx 3.93 \)[/tex]
- The intercept [tex]\( b \approx 28.91 \)[/tex]
So, the regression equation is:
[tex]\[ y = 3.93 \cdot x + 28.91 \][/tex]
### Step 2: Predict the Final Grade
Now, we want to predict the final grade for a student who spends an average of 13 hours per week on math. Using the regression equation:
Substitute [tex]\( x = 13 \)[/tex] into the equation:
[tex]\[ y = 3.93 \cdot 13 + 28.91 \][/tex]
Calculate the value:
[tex]\[ y = 51.09 + 28.91 \][/tex]
[tex]\[ y \approx 80.0 \][/tex]
Therefore, the predicted final grade when a student spends an average of 13 hours each week on math is approximately 80.0 when rounded to 1 decimal place.
Thank you for reading the article Run a regression analysis on the following data set where tex y tex is the final grade in a math class and tex x tex. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
