To determine the sample regression equation and the predicted salary for an individual with seven years of education, let's proceed with these steps:

1. Calculate the Sample Regression Equation: The regression model is given by: $\text{Salary} = B_0 + B_1 \times \text{Education} + \varepsilon$ We need to find the values of $B_0$ (the intercept) and $B_1$ (the slope) using the data provided.

2. Extract Data: I will retrieve the salary and education data from the image and calculate the necessary statistical values, including the mean of Salary and Education, and the covariance and variance required for computing $B_1$ and $B_0$.

3. Calculate $B_0$ and $B_1$:

   • $B_1 = \frac{\text{Cov}(\text{Education, Salary})}{\text{Var(Education)}}$
   • $B_0 = \bar{Y} - B_1 \times \bar{X}$

4. Prediction: After determining $B_0$ and $B_1$, substitute $\text{Education} = 7$ into the equation to predict the salary.

I'll now proceed with the calculations and provide the regression equation and prediction for an individual with seven years of education.The sample regression equation based on the provided data is:

$\text{Salary} = 21.76 + 10.77 \times \text{Education}$

Using this equation, the predicted salary for an individual who has completed seven years of education is approximately:

$97.12 \text{ dollars}$

Would you like a more detailed breakdown of each calculation step, or do you have any further questions?

Here are some related questions for deeper exploration:

1. How would the regression equation change if we removed outliers in the data?
2. What does the slope $B_1$ of 10.77 signify in terms of salary increase per year of education?
3. How can we assess the goodness of fit of this regression model?
4. Would using a different model (e.g., polynomial regression) provide a better fit for this data?
5. How might additional variables (e.g., experience) impact the model's accuracy?

Tip: Always check the residuals of your regression model to ensure that the assumptions of linear regression are reasonably met.