I am trying to double check my answer, I completed a spatter blot of an assignment, 20 student, variables study hours and final exam scores, the two I am suppose to predict would be study hours of 5 and study hours of 11. How would I put that in an equation to predict the exam scores? Thank you

find the standard deviation by substituting n= 147, p=0.13 and q=0.87

4.1

To predict the exam scores based on study hours, you can use linear regression. Linear regression finds a linear relationship between the independent variable (study hours) and the dependent variable (exam scores). Here's how you can formulate the equation:

1. Start by organizing your data into two columns: one column for study hours and the other for exam scores for the 20 students.

2. Calculate the mean (average) of both the study hours and exam scores. Let's say the mean study hours is denoted as x̄ and the mean exam score as ȳ.

3. Calculate the standard deviation of both the study hours (denoted as sx) and exam scores (denoted as sy).

4. For each student, calculate the difference between their study hours and the mean study hours (x - x̄).

5. Similarly, calculate the difference between their exam score and the mean exam score (y - ȳ).

6. Multiply the differences from step 4 and 5 for each student. For example, for the first student, multiply (x1 - x̄) and (y1 - ȳ), and so on for all the students.

7. Calculate the sum of the multiplied differences.

8. Calculate the square of the standard deviation of study hours.

9. Using the sum from step 7 and the squared standard deviation from step 8, calculate the slope (b) of the linear regression equation using the formula: b = sum of multiplied differences / squared standard deviation of study hours.

10. Using the mean study hours (x̄), mean exam score (ȳ), and the slope (b), write the equation of the regression line: y = b * (x - x̄) + ȳ.

Now, to predict the exam scores for study hours of 5 and 11, substitute these values into the regression equation:

For study hours of 5: predicted exam score = b * (5 - x̄) + ȳ

For study hours of 11: predicted exam score = b * (11 - x̄) + ȳ

By plugging in these values, you can calculate the predicted exam scores based on the linear regression model.