To insert the predicted values for the given cases using a regression equation, we need the regression equation itself. The general form of a linear regression equation is:

$\text{Predicted Final Exam Score} = a + b \times (\text{First Exam Score})$

Where $a$ is the intercept and $b$ is the slope of the regression line.

Without the specific values of $a$ and $b$, I cannot calculate the exact predicted values. However, if you provide the regression equation (or the values for $a$ and $b$), I can use it to find the predicted final exam scores for the given first exam scores.

Assuming we have a regression equation of the form:

$\text{Final} = a + b \times \text{First}$

Where:

• $\text{First}$ is the score on the first exam
• $\text{Final}$ is the predicted score on the final exam

Let's assume the values of $a$ and $b$ are as follows (for illustration purposes): $a = 10$ $b = 0.8$

Now, let's compute the predicted values for the given cases:

1. First Exam: 62 $\text{Predicted Final} = 10 + 0.8 \times 62 = 10 + 49.6 = 59.6$ Rounded to three decimal places: $59.600$

2. First Exam: 77 $\text{Predicted Final} = 10 + 0.8 \times 77 = 10 + 61.6 = 71.6$ Rounded to three decimal places: $71.600$

3. First Exam: 98 $\text{Predicted Final} = 10 + 0.8 \times 98 = 10 + 78.4 = 88.4$ Rounded to three decimal places: $88.400$

If you provide the specific regression equation or the values of $a$ and $b$, I can give you the accurate predicted values.

Do you have any questions or need further details on how this calculation was made? Here are five more questions you might find helpful:

1. How do I determine the slope and intercept of a regression line?
2. Can you explain how to calculate the correlation coefficient?
3. What is the difference between simple and multiple linear regression?
4. How do I interpret the results of a regression analysis?
5. What are some common pitfalls in regression analysis and how can I avoid them?

Tip: Always check the assumptions of regression analysis (such as linearity, independence, homoscedasticity, and normality) to ensure the validity of your model.